let NAN = 0;; let searchd pat = searchl (map (fun t -> ("",t)) (definitions())) pat;; let ineq_as_thm = map (fun t -> t.idv,ASSUME t.ineq) (!Ineq.ineqs);; let prep_as_thm = map (fun t -> t.idv,ASSUME t.ineq) (!Prep.prep_ineqs);; let searchi pat = searchl (ineq_as_thm) pat;; let searchp pat = searchl (prep_as_thm) pat;; Sphere.vol2r;; Sphere.vol2f;; Sphere.gamma23f;; Sphere.a_spine5;; Sphere.b_spine5;; Sphere.gamma3f;; Sphere.vol3f;; vol3f_palt;; search[`vol3f`];; search[`gchi`];; search[`delta_x`;`eta_x`];; vol3f_x_sqrt2_lmplus;; vol3f_x_lfun;; vol3_x_sqrt;; vol3f_palt;; help_grep "GEN";; Sphere.eta2_135;; ineq;; Sphere.vol3r;; searcht 5 [`lfun`];; cpp_string_of_term `#3.0`;; chop_list 3 [`a`;`b`;`c`;`d`];; Parse_ineq.autogen;; let ineq = Sphere.ineq;; let all_forall = Sphere.all_forall;; split_ineq;; Sphere.vol3r;; Sphere.vol_x;; (* *) Sys.command("pwd");; search[`vol3f`];; search[`sqrt2`];; search[`dihRy`];; search[`solRy`];; search[`lmfun`;`lfun`];; search[`lmfun`;`h0`];; Sphere.dih_x;; Sphere.atn2;; Sphere.vol_x;; Sphere.vol4f;; Sphere.gamma4f;; search [`lfun`];; search [`ly`];; searcht 3 [`matn`];; type_of `matan`;; Sphere.vol4f;; help "dest_binder";; help_grep "binder";; help "is_binder";; binders();; Sphere.arclength;; searcht 5 [`acs`;`atn`];; searcht 5 [`acs`;`asn`];; Sphere.a_spine5;; Sphere.atn2;; Sphere.dih_x;; Sphere.vol3r;; Sphere.vol_x;; Sphere.vol3f;; Sphere.sol_y;; searcht 5 [`sol_y`;`atn`];; searcht 20 [`delta_x4`];; search [name "Euler"];; it;; Sphere.gamma3f;; Sphere.vol3f;; Sphere.gamma23f;; Sphere.vol2r;; Sphere.marchal_quartic;; Sphere.taum;; Sphere.lnazim;; Sphere.rhazim;; Sphere.rho;; Sphere.rhazim;; Sphere.ly;; Sphere.const1;; Sphere.vol4f;; Sphere.vol_y;; Sphere.const1;; Sphere.lfun;; Sphere.lmfun;; Sphere.mm1;; Sphere.mm2;; Sphere.rhazim2;; Sphere.sol0;; Sphere.edge_flat;; Sphere.vol2r;; Sphere.vol2f;; Sphere.mm1;; Sphere.mm2;; Sphere.tau0;; Sphere.marchal_quartic;; Sphere.hplus;; searcht 100 [`asn`;`atn`];; searcht 100 [`rhazim2`];; searcht 100 [`sol0`];; Sphere.arclength;; REAL_FIELD;; search[`];; search[`&0 < sol0`];; Sphere.edge_flat;; Sphere.flat_term;; Sphere.tame_table_d;; search[`radV`];; Sphere.gamma4f;; Sphere.rad2_y;; Sphere.rad2_x;; Parse_ineq.y_of_x_e;; Sphere.vol_x;; Sphere.dih6_y;; gchi1_x;; gchi;; dih4_x;; List.length !Ineq.ineqs;; Sphere.atn2;; "string";; curry;; search [name "Packing"];; help_grep "list";; help "chop_list";; Sphere.gamma4f;; Sphere.vol4f;; Sphere.vol3f;; Sphere.vol2f;; Sphere.ups_x;; Sphere.quadratic_root_plus;; searcht 10 [`edge_flat`];; searcht 10 [`(sqrt x) pow 2`];; searcht 4 [`abs`;`sqrt`];; searcht 5 [`sqrt x pow 2`];; SQRT_POW_2;; help_grep "REWRITE_TAC";; (* Sphere.beta_bump_y;; Sphere.bump;; Sphere.lmfun;; Sphere.beta_bump_force_y;; Sphere.critical_edge_y;; Sphere.vol4f;; Sphere.hminus;; Sphere.h0;; Sphere.hplus;; *) search[`vol4f`;`lmfun`];; search[`gcy`;`gchi`];; search[`gcy`];; ineq_expand;; help_grep "REP";; search [name "cycle_";];; help "REPEATC";; help "MATCH_MP";; help_grep "CHANGED";; search[name "MVT"];;"MVT_GENERAL";; search[name "IVT"];; REAL_IVT_DECREASING;; REAL_IVT_DECREASING;; search[`real_continuous_on`];;"REAL_CONTINUOUS_ON_NEG","REAL_CONTINUOUS_ON_MUL","REAL_CONTINUOUS_ON_POW",("REAL_CONTINUOUS_ON_LMUL"),"REAL_CONTINUOUS_ON_SUB","REAL_CONTINUOUS_ON_RMUL","REAL_CONTINUOUS_ON_ID","REAL_ROLLE","REAL_CONTINUOUS_ON_ADD","REAL_CONTINUOUS_ON_CONST"; (* also REAL_CONTINUOUS_MUL, REAL_CONTINUOUS_SUB, etc. *) REAL_CONTINUOUS_ON_POW;; searcht 5 [`has_real_derivative`;`u + v`],"HAS_REAL_DERIVATIVE_ADD";; search [name "HAS_REAL_DERIVATIVE"];; "HAS_REAL_DERIVATIVE_INCREASING_IMP","HAS_REAL_DERIVATIVE_CONST","HAS_REAL_DERIVATIVE_POW_ATREAL",("HAS_REAL_DERIVATIVE_POW_WITHIN"),"HAS_REAL_DERIVATIVE_INCREASING","HAS_REAL_DERIVATIVE_ADD","HAS_REAL_DERIVATIVE_ID", search[`has_real_derivative`;name "MVT"];; REAL_ROLLE;; HAS_REAL_DERIVATIVE_INCREASING;; searcht 10 [`has_real_derivative`;`f x < f y`];; REAL_ROLLE;; searcht 5 [`&0 <= a /\ &0 <= b ==> &0 <= a * b`];; searcht 5 [`(a /\ b) /\ c` ; `a /\ b /\ c`];; searcht 5 [`#1.2`;`hminus`]; hminus_prop;; searcht 5 [`rhazim_x`];; rhazim_x;; rhazim2_x;; searcht 5 [`(\x. f (x) * g x) real_continuous_on s`];; searcht 10 [`inv (x * y)`;`inv x * inv y`];; searcht 10 [`inv(inv x)`];; searcht 5 [`&0 <= inv (x) <=> &0 <= x`];; searcht 10 [`x ==> (&0 < u / v)`];; searcht 10 [`x < t /\ t <= u ==> x < u`];; searcht 10 [`x pow 2 < y pow 2`];; searcht 10 [`x ==> (&0 <= u/v)`];; searcht 5 [`lmfun`;`lfun`];; Sphere.marchal_quartic;; Sphere.lmfun;; Sphere.hminus;; searcht 5[`FST a,SND a`],PAIR;; searcht 5 [`sol0`];;GSYM Tame_general.sol0_over_pi_EQ_const1 searcht 5 [`&0 < pi`],PI_POS; searcht 4 [` (x * y) pow n`];;REAL_POW_MUL;; searcht 10 [`x * inv y`];; searcht 10 [`sqrt8`;`sqrt2`];; searcht 5 [`sqrt ( x pow 2)`];; searcht 5 [`sqrt (x ) * sqrt(a)`];; searcht 10 [`&0 <= sqrt (x)`],SQRT_POS_LE;;; search [name "TAYLOR"];; search [name "GRAD"];; (search [`x pow 2 <= y pow 2 `],Collect_gome.POW2_COND);; searcht 10 [`(sqrt x) pow 2`],Collect_geom.POW2_COND;; searcht 10 [`&0 <= a pow 2`],Collect_geom.REAL_LE_SQUARE_POW;; searcht 10 [`abs b pow 2 = b pow 2`];; searcht 10 [`x <=y /\ y <= z ==> P`],REAL_LE_TRANS;;; searcht 10 [`&0 <= sqrt x`],Collect_geom.REAL_LE_SQUARE_POW;; (search [`x pow 2 <= y pow 2 `],SQRT_POW2);; searcht 10 [`x pow 2 = x * x`], REAL_POW_2;; searcht 10 [`x pow 2 <= y pow 2`];; searcht 10 [`sqrt(y pow 2)`];; search[`sqrt(a*b) = sqrt a * sqrt b`],SQRT_MUL;; search[`sqrt(a pow 2 * b)`];; search[`sqrt(x pow 2)`],POW_2_SQRT_ABS;; search[`acs`;`atn`],ACS_ATN;; search[`atn`;`pi`],ATN_1;; search[`pi`;`atn`],ATN_1;; search[`interval_eps (float a b) r e`];; search[`real_of_int (& n)`];; search[`twopow (-- (int_of_num n))`],Float.TWOPOW_NEG;; search[`x:1`];; search_thml (term_match []) [(concl Hypermap.lemma_mAdd)] (map (fun t -> ("",t)) (definitions()));; search!definitions searcht 10 [`pi`;`atn`];; searcht 10 [`atn`;`halfatn4`];; search[`acs`;`atn`];; searcht 10[`atn`;`pi`];; searcht 10 [`ssqrt`];; search[`!i. 1 <= i /\ i <= 3 ==> vec 1$ i = &1`];; searcht[`x <= y /\ y <= z ==> x <= z`];; search[`atn`];; search[`cos`];; search[`sin`;`FACT`];; search [`sum (:num)`];; search[`has_real_derivative`;`atn`];; (* HAS_REAL_DERIVATIVE_ATN *) search[`binom`];; search[`has_real_derivative`;`Re`];; (* HAS_REAL_COMPLEX_DERIVATIVE_AT *) search[`has_complex_derivative`];; search[`atn`;`catn`];; (* yes *) search[`dihX3`];; search[`sin x = t`];; search[`mcell_set`];; search[`dihV a b c d = dihV a' b' c' d'`];; search[`facet_of`];; searcht 5[`aff_ge`];; searcht 5[`sum X f = &0`], SUM_TRIV_NUMSEG;; search [`sum (i..SUC j) f`], CONJUNCT2 SUM_CLAUSES_NUMSEG;; search [`sum (i..i)`],SUM_SING_NUMSEG;; searcht 5[`sum (i..j) f`;`i< j`];; search[`sum (SUC i..j) f`];; search[`fan80 (x,V,E) = y`];; search[`fan81 (x,V,E) = y`];; search[`let x = (y:A) in (z:B)`];; search[`let x = y in z`];; search[name "CZZH"];; fst(List.nth (search[full `sqrt(&x) = y`]) 0);; search[full `!x y. x + y = y + x`];; search[`sqrt`;omit `x:num`];; search[];; search[exactly `a + b = b + a`];; search[full `!a b. a + b = b + a`];; search[`x:hypermap`];; search[`sqrt(&x) = y`];; search [`sum (i..SUC j)`];; Searching.suggest();; search[`abs(atn u - &16 *x)`];; search[`abs(x + y) <= abs(x) + abs y`],REAL_ABS_TRIANGLE;; help_grep "mk_n";; help "instantiate";; help "INSTANTIATE";; help_grep "TERM";; help "AP_TERM";; help_grep "DISCH";; help "UNDISCH";; help_grep "conj";; help_grep "mk.*eq";; help_grep "ty.*var";; help_grep "ty";; help_grep "strip";; help_grep "_TAC$";; help_grep "^ASM";; help "PROVE_HYP";; help "EQ_MP";; help "AP_TERM";; Searching.help_grep "AP_";; help "striplist";; help"MK_CONJ";; help "META_EXISTS_TAC";; help "UNIFY_ACCEPT_TAC";; help_grep "PURE_";; help "BETA_CONV";; help_grep "ARITH";; (* g `(P:num-> bool) ( @ t. t >0)`;; g `(a /\ b) ==> c`;; g `(a \/ b) ==> c`;; g `(?x . t) ==> c`;; g `(f:A->B) = g`;; g `(x:A->B) = g`;; g `sqrt(&3) < sqrt(&4)`;; g `?x. f x`;; DISCH_TAC; s 0;; eh 1;; eh 0;; eh 0;; eh 1;; suggest();; g `?x. f x`;; g `(f:A->B) =g`;; *) (* termination tactics MESON, REAL_ARITH, SET_TAC, ARITH_TAC;; REAL_FIELD, REAL_RING, SIMPLE_COMPLEX_ARITH_TAC; REAL_LET_TRANS;; FORALL_PAIR_THM;; REWRITE_TAC[FORALL_PAIR_THM];; EXISTS_PAIRED_THM;; REWRITE_TAC[GSYM EXISTS_PAIRED_THM] ;; *) (* IMP_RES_THEN forward implications of assumption list *) (* MATCH_ACCEPT_TAC goal is instance of supplied theorem PATH_CONV, find_path, follow_path PAT_CONV (can be used on swapping quantifiers! ) POP_ASSUM, POP_ASSUM_LIST REPLICATE_TAC n GEN_TAC RULE_ASSUM_TAC (maps an inference rule over assumption list) RULE_ASSUM_TAC (TRY (CHOOSE_)) SUBST1_TAC, SUBST_ALL_TAC. *) (* NAMED ASSUMPTIONS *) (* theorem usage. rewrites, simplifications, introductions, definitions, assume ispecl, *) (* amplifications, curtailments, *) (* terminators. *) (* quants. *) (searcht 5 [`x pow (a + y) = x pow a * x pow y`],REAL_POW_ADD);; (searcht 5 [`x pow 1`],REAL_POW_1);; searcht 5 [`x pow 0`],(CONJUNCT1 real_pow);; (* some searches that came up in practice. *) Searching.suggest();; search[`atn has_real_derivative z`];; searcht 10[name "WITHIN";`atreal`;`has_real_derivative`],"HAS_REAL_DERIVATIVE_ATREAL_WITHIN"; searcht 3[name "MVT";`has_real_derivative`],REAL_MVT_VERY_SIMPLE;; searcht 5 [`inv (x * y ) = inv (x ) * inv (y)`],REAL_INV_MUL;; searcht 5 [`z pow (a + b) = z pow a * z pow b`],REAL_POW_ADD;; searcht 5 [`(z pow a) pow b = z pow (a * b)`];; searcht 8 [`halfatn`],halfatn_bounds_abs;; searcht 8 [`atn(halfatn x)`];; halfatn_half; searcht 8 [`&0 <= abs(x)`],REAL_ABS_POS;; searcht 8 [`inv (x pow k)`],REAL_INV_POW;; search[`x pow k <= y pow k`],Real_ext.REAL_PROP_LE_POW; search[`&0 <= x pow 2`];; search[`inv x <= inv y`];REAL_LE_INV2;; search[`&0 <= abs(x)`],REAL_ABS_POS;; search[`abs(inv x)`;`inv(abs x)`],REAL_ABS_INV;; search[`abs(x * y) = abs(x) * abs y`],REAL_ABS_MUL;; search[`x * y <= x * z`],REAL_LE_LMUL;; searcht 5 [`EVEN`;`ODD`],NOT_EVEN;; searcht 5 [`~(?x. P)`],NOT_EXISTS_THM;; searcht 10 [`(=) (a..b)`],numseg;; searcht 3[`sum (IMAGE f X)`],SUM_IMAGE;; searcht 3[`sum`;`SUBSET`;`&0`],SUM_SUPERSET;; search[`m/m = &1`],REAL_DIV_REFL;; search [`&x = &y`;`(x:num) = y`],REAL_OF_NUM_EQ;; searcht 4 [`& (x * y)`; `& x * & y`],REAL_OF_NUM_MUL;; searcht 4 [`ODD`;`2 * k`], ODD_EXISTS;; searcht 4 [`EVEN`;`ODD`],NOT_EVEN;; search[`norm (Cx x)`],COMPLEX_NORM_CX;; search[`Cx x pow i`],CX_POW;; search[`Cx a - Cx b`],CX_SUB;; search[`Cx (x) * Cx (y)`],CX_MUL;; search[`Cx(x)/Cx(y)`],CX_DIV;; searcht 5 [`f (if x then y else z)`;`(if x then f y else f z)`];; "not found" search[`Im (Cx x)`];; search[`catn`;`atn`],GSYM CX_ATN;; search[`taylor_coeff_catn`;`DIV`],taylor_coeff0;; (searcht 10 [`Im z = &0`;`Cx`],"not found" (Im z = &0 <=> (?x. z = Cx(x))));; search[`Im (Cx x) = &0`],IM_CX;; search[`(x:num) > y <=> y < x`],GT;; search [`0 < FACT n`],FACT_LT;; search[`(&x = &y) = (x = y)`],REAL_OF_NUM_EQ;; (search[`((a:real) * b /a = b)`],REAL_DIV_LMUL); (search[`taylor_coeff_catn 0`],taylor_coeff_catn0);; search[`taylor_coeff_catn`;`has_complex_derivative`];; (* -- hard one to find. (at x) (at x within y) *) ([`at x within y`,`has_complex_derivative`],HAS_COMPLEX_DERIVATIVE_AT_WITHIN); (search[`Im ( v % x )`],IM_CMUL); (`Im (x + y)`,IM_ADD); (`&1 pow n`,REAL_POW_ONE); (`abs( -- x)`,REAL_ABS_NEG); (`abs(&n)`,REAL_ABS_NUM); [ (`norm((a:real^A) + b) <= norm (a) + norm(b)`,"NORM_TRIANGLE",NORM_TRIANGLE);; ];; MATCH_MPlist: [ (`((a:real) <= c ) /\ (b <= d) ==> (a + b <= c + d)`,"REAL_LE_ADD2",REAL_LE_ADD2); ];; num_CASES;; search[`norm(a-b)`;`dist`];; search[`0 <= FACT n`];; search[`norm(inv(a))`];; search[`&a <= &b`;`(a:num) <= (b:num)`];; search[`norm (a * b) = norm (a) * norm (b)`];; search[`norm ii`];; search[`norm (z pow k)`];; search[`norm (Cx a)`];; search[`norm(inv z)`];; COMPLEX_NORM_POW;; COMPLEX_NORM_INV;; search [`(z:real) pow (a + b)`];; search[`z pow (a + b)`];; search[`EVEN`;`2*m`];; search[`atn (&0)`];; search[`catn`;`atn`];; search[`EVEN`;`ODD`];; search[`Cx(&1) pow n`];; search[`Cx (a * b)`];; search[`z pow 0`];; search[`vsum`;`sum`;`Cx`],VSUM_CX_NUMSEG;; VSUM_CX_NUMSEG;; search[`has_complex_derivative`;`has_real_derivative`];; COMPLEX_TAYLOR;; HAS_COMPLEX_REAL_DERIVATIVE_AT;; ([`vsum`;`sum`;`Cx`],VSUM_CX_NUMSEG);; ([`vsum:(num->bool) -> (num->complex)->complex`;`sum`],VSUM_CX_NUMSEG);; type_of `vsum`;; (* counting_spheres *) (* PRESERVES_NORM_INJECTIVE;; MEASURABLE_LINEAR_IMAGE_EQ;; RADIAL_NORM_LINEAR_INVARIANT;; linear_inter_normball;; search [`solvec0`];; searcht 10 [`radial`];; Marchal_cells_2.RADIAL_VS_RADIAL_NORM;; searcht 1 [`radial_norm`];; searcht 0 [`linear`;`radial_norm`];; MEASURABLE_LINEAR_IMAGE_EQ;; searcht 15 [`measurable`;`linear`];; Vol1.sol;; searcht 15 [`sol`];; searcht 10 [`measurable (a INTER b)`];; *) (* Vol1.sol;; sol0_linear_r;; linear_inter_normball;; MEASURE_LINEAR_IMAGE_SAME;; search[`vol`;`measure`];; Marchal_cells_2.RADIAL_VS_RADIAL_NORM;; search[`linear`;`measurable`];; Vol1.sol;; search[`radial_norm`];; sol;; SUBGOAL_TAC;; SUBGOAL_THEN;; search[`linear`;`t % f u`];; type_of_goal ();; help "apropos_types";; PRESERVES_NORM_INJECTIVE;; searcht 15 [`norm u = norm v`;`(f x = f y) ==> (x = y)`];; searcht 5 [`<=>`;`(A ==> b) /\ (b ==> A)`];; srch[`dist`;`norm`];; ball;; srch[`ball`];; srch[`X SUBSET ball(u,r)`];; srch[`vec 0 + x`];; srch;; srch [`IMAGE f x SUBSET IMAGE f t`];; srch [`vec 0 + x`];; type_of `radial_norm`;; *) (* Work in progress def_of_regexp "radial$";; def_of_regexp "radial_norm";; def_of_regexp "radial$";; srch [`eventually_radial`];; srch [`radial_norm`];; more();; srch [`normball`;`ball`];; search [`sol`];; Vol1.sol;; type_of `sol`;; type_of_thm LINEAR_CMUL;; type_of_goal();; linear;; srch [`f (t % u)`;`linear`];; help "ISPECL";; RELATIVE_INTERIOR_INJECTIVE_LINEAR_IMAGE;; srch [`relative_interior (IMAGE f c)`];; Polyhedron.fchanged;; search_thml (term_match []) [`sol`] (map (fun s -> ("",s)) (!invariant_under_linear));; srch [`fchanged`];; *) (* add_linear_invariants;; *) (* add_linear_invariants [FCHANGED_LINEAR_INVARIANT ; LINEAR_0;RCONE_LINEAR_INVARIANT ];; *) (* searcht 15 [`rcone_gt`];; more();; def_of_regexp "rconesgn";; help_grep "without";; searcht 5 [`dropout`];; searcht 5 [`azim`;`Arg`];; type_of `hypermap_of_fanx`;; def_of_regexp "wedge";; def_of_regexp "cyclic_set";; search [`wedge_ge`;];; search [`azim v1 v2 x y + azim v1 v2 y z`;name "sum"];; search [`wedge_ge`];; search [`cwedge`];; search [`cw_dart_fan`];; search [`cwedge`];; search [`fan`];; search [`FAN`];; *) (* a polyhedral bound *) (* February 2012 searches *) results[];; mark 0;; Calc_derivative.rational_identity `b / a * a = b`;; searcht 5 [`face_of`;`t % v`];; searcht 5 [`v dot v`;`&0`];; mark 3;; searcht 5 [`a dot (vec 0)`];; mark 0;; searcht 15 [`facet_of`;`{}`];; mark 1;; searcht 5 [`(a % b) dot c`];; searcht 15 [`rcone_gt`];; mark 1;; searcht 5 [`x:real^3`;`x dot y = &0`];; EUSOTYP_general;; 1;; searcht 5 [`pad2d3d x = pad2d3d y`];; mark 0;; searcht 5 [`vec 0`;`Cx (&0)`];; searcht 5 [`norm (facet_rep_a P c)`];; mark 1;; searcht 5 [`Cx u = Cx v`];; searcht 5 [`norm x = r`];; searcht 5 [`norm (vec 0)`];; searcht 5 [`-- &1`;`aff_dim p`];; searcht 5 [`polytope`;`polyhedron`];; mark 4;; facet_arg_lt_pi;; !search_results;; results[];; mark 0;; searcht 10 [`convex`;`polytope`];; searcht 10 [`(?)`;`extreme_point_of`];; searcht 10 [def "extreme"];; searcht 10 [`extreme_point_of`;`face_of`];; searcht 10 [`?`;`face_of`];; searcht 15 [`X = {}`;`IN`];; searcht 5 [`u HAS_SIZE 0`];; 1;; searcht 15 [`radial_norm`];; searcht 15 [`fchanged`;`radial_norm`];; searcht 15 [`fchanged`;`radial`];; searcht 15 [`fchanged`;`eventually_radial_norm`];; searcht 15 [`wedge`;`radial_norm`];; searcht 15 [`wedge`;`radial`];; searcht 15 [`wedge`;`eventually_radial_norm`];; searcht 15 [`wedge`;`sol`];; searchn 0 [`sol`;`UNION`] "Conforming.SOL_DISJOINT_UNION";; searchn 1 [`sol`;`UNIONS`] "Conforming.SOL_UNIONS";; searchn 0 [`sol`;`UNIONS`] "Conforming.SUM_SOL_TOPOLOGICAL_COMPONENT_YFAN_EQ_SOL_UNIONS";; searcht 15 [`sol`];; searchn 2 [`sol`] "Conforming.SOLID_ANGLE_YFAN";; (* 4 Pi sum *) searcht 5 [`fchanged`;`sol`];; searchn 0 [`open`;`measurable`] "MEASURABLE_OPEN";; searcht 10 [`fchanged`];; search [name "AMHFNXP"];; searcht 5 [`sum (n..n)`];; searchn 2 [`sum X f = sum X g`] "SUM_EQ";; SUM_ADD_SPLIT;; SUM_PAIR;; searcht 15 [`sum`;`(a..( n+m))`];; searcht 15 [name "SUM_DIFF"];; searchn 0 [`sum`;`\i. (f (i+1) - f (i))`] "SUM_DIFFS_ALT";; searcht 15 [name "TELE"];; searcht 15 [`azim`;`sum`];; AZIM;; searcht 5 [`&0 <= azim x y z w`];; AZIM_BASE_SHIFT_LT;; X_IN;; X_GEN_TAC;; help_grep "GEN";; search [`p IN {}`];; REAL_WLOG_LE;; AZIM_BASE_SHIFT_LT;; search[`cyclic_set`];; Fan.sum4_azim_fan;; (* lower ineq *) Fan.sum5_azim_fan;; (* upper ineq *) Counting_spheres.EUSOTYP_general;; searcht 5 [`azim a b c d < azim a b c' d'`];; searcht 5 [`&0 <= azim a b c d`];; searchn 1 [`azim`;`&2 * pi`] "Local_lemmas.AZIM_RANGE";; searchn 2 [`azim`;`&2 * pi`] "Rogers.AZIM_COMPL_EXT";; searcht 10 [`azim`;`&2 * pi`];; searcht 25 [`wedge`];; searcht 5 [`sum`;`azim`];; searchn 3 [`azim a b c d + azim a b c' d'`] "Fan.sum5_azim_fan";; searcht 50 [`azim a b c d + azim a b c' d'`;omit `cyclic_set`];; vol_solid_triangle_ortho;; vol_solid_triangle;; searcht 5 [`vol_solid_triangle`];; searcht 5 [name "solid_triangle"];; searcht 5 [name "cone0"];; searcht 5 [name "normball"];; searcht 5 [`ball`;`( < )`];; 1;; searcht 5 [`x IN IMAGE (dropout 3) U`];; pad2d3d_dot;; VECTOR_ARITH;; linear;; LINEAR_NEG;; searcht 65 [def "linear"];; searcht 15 [`linear`;`f (x:real^A) + f y`];; searcht 15 [`linear`;`pad2d3d`;LINEAR_PAD2D3D];; searcht 15 [`pad2d3d`;`(x:real^2)`];; searcht 5 [`pad2d3d`;`dot`];; types_of (concl pad2d3d_dot);; EUSOTYP_simple;; (* searcht 5 [`(z:complex) * u = u * z`];; searcht 5 [`Arg (Cx r * u)`];; searcht 5 [`cnj (x * y)`];; searcht 5[ `cnj`;`Cx`];; searcht 5 [`Cx x = Cx y`];; searcht 5 [`z * u = Cx(&0)`];; ASM_CASES_TAC;; searcht 5 [`inv( Cx (&0))`];; *) asimp[sym Ysskqoy.COS_ARG_VECTOR_ANGLE] amt[Ysskqoy.COS_ARG_VECTOR_ANGLE;COMPLEX_ENTIRE;CX_INJ;arith `&0 < r ==> ~(r = &0)`] searcht 5 [`Cx u = Cx v`];; searcht 15 [`norm x = &0`];; searcht 15 [`pi = &0`];; searcht 15 [`cos x = &0`];; searcht 5 [`inv x = &0`];; Ysskqoy.COS_ARG_VECTOR_ANGLE;; searcht 5 [`vector_angle u v = vector_angle v u`];; GSYM Ysskqoy.SEC_DOT;; searcht 5 [`norm (facet_rep_a P c)`];; searcht 5 [`norm (Cx r)`];; searcht 5 [`(x:complex)/ x`];; facet_arg_lt_pi;; searcht 5 [` x HAS_SIZE 1`];; facet_arg_lt_pi;; POLY_SORT_BIJ;; searcht 5 [`inv (Cx u)`];; ARG_MUL_CX;; searcht 5 [`inv (a * (b:complex))`];; searcht 5 [`Arg`; `Cx`];; searcht 5 [`(z:complex) * w`;`r % u`];; searcht 5 [`facet_rep_a`;`&0`];; mt[] art[] POLYSORT_BIJ2;; suggest();; Counting_spheres.facet_rep_nz;; searcht 5 [`Arg (Cx (&n))`];; searcht 5 [`(x:complex)/x`];; POLYTOPE_FACET_EXISTS;; searcht 5 [`(?)`;`facet_of`];; searcht 5 [`facet_rep_a P u = Cx (&0)`];; SPECL [`u:real^2`;`h = \(i:num). facet_rep_a P (if i IN 1..n then f i else f 1)`;`n:num`] ARG_ORDER;; types_of `h = \(i:num). facet_rep_a P (if i IN 1..n then f i else f 1)`;; type_of_thm ARG_ORDER;; ARG_ORDER;; searcht 5 [`&0 <= Arg z`];; ARG_INV_ALT;; REAL;; complex_frac_cancel;; SIMPLE_COMPLEX_ARITH;; help_grep "COMPLEX.*TAC";; searcht 5 [`Cx (&1) * b = b`];; searcht 5 [`inv b * b = Cx (&1)`];; complex_div;; searcht 0 [`inv (a:complex/b)`] "COMPLEX_INV_DIV" ;; searcht 5 [`((a:complex)/b)/(c/d)`];; searcht 5 [`Arg ((x/y)/(z/y))`];; searcht 5 [`Arg (x/y)`];; searchn 0 [`a /b = Cx (&0)`] "Ysskqoy.ARG_0_DIV";; ARG_LE_DIV_SUM;; searcht 0 [` (inv (z/(u:complex)))`] "COMPLEX_INV_DIV";; searchn 0 [`&0 <= Arg z`] "ARG";; searcht 5 [`facet_of`;`polyhedron`;`HAS_SIZE`];; SEC_DOT;; searcht 20 [`wedge`];; searcht 10 [`Arg (z) + Arg (w) `];; facet_arg_lt_pi;; searcht 10 [`bisector_point`];; searcht 10 [`norm (Cx (&0))`];; searcht 10 [`Arg`;`Cx`];; searcht 10 [`( * ):real^2->real^2->real^2`;`(%)`];; searcht 10 [`Arg`;`(%)`];; dest_const `(..)`;; searcht 10 [`(..)`;`IN`];; searcht 5 [`&0 < r`;`abs r = r`];; searcht 5 [`norm (a % v)`];; type_of `facet_rep_a`;; searchn 3 [`facet_rep_a`] "Counting_spheres.facet_rep_in_poly";; searchn 9 [`facet_rep_a`] "Counting_spheres.facet_arg_lt_pi";; searchn 10 [`facet_rep_a`] "Counting_spheres.facet_rep_def";; (* rep has norm 1 *) POLYHEDRON_LINEAR_IMAGE;; Ysskqoy.COS_ARG_VECTOR_ANGLE;; bisector_point;; Ysskqoy.SEC_DOT;; searchn 0 [`BIJ`;`HAS_SIZE`] "Counting_spheres.POLY_SORT_BIJ";; searcht 10 [`pad2d3d`];; searcht 10 [`aff_dim`;`plane`];; searcht 10 [`affine`;`SUBSET`];; pad_in;; searcht 15 [`IN`;`SUBSET`];; searcht 15 [`pad2d3d`];; searchn 0 [`Cx (&0)`;`vec 0`] "COMPLEX_VEC_0";; searcht 5 [`x SUBSET x`];; searcht 5 [`SUBSET`;`facet_of`];; searcht 5 [`IMAGE h x = x`];; searcht 5 [`IMAGE f (IMAGE g x)`];; BIJECTIONS_HAS_SIZE;; searchn 0 [`linear`;`facet_of`] "FACET_OF_LINEAR_IMAGE" ;; searcht 5 [`dropout`;`(f x = f y) ==> (x =y)`] (* none *);; searchn 0 [`dropout`;`linear`] "LINEAR_DROPOUT";; searcht 15 [`dropout`;`face_of`] ;; PRESERVES_NORM_INJECTIVE;; searcht 5 [`dropout`;`norm`];; (* none *) searcht 15 [`(f x = f y) ==> (x = y)`;`HAS_SIZE`];; searchn 0 [`pad2d3d`;`linear`] "LINEAR_PAD2D3D";; AZIM_SPECIAL_SCALE;; PRESERVES_NORM_INJECTIVE;; NORM_PAD2D3D;; searchn 0 [`linear`;`polyhedron`] "POLYHEDRON_LINEAR_IMAGE";; searchn 0 [`linear`;`bounded`] "BOUNDED_LINEAR_IMAGE";; searchn 0 [`pad2d3d`;`linear`] "LINEAR_PAD2D3D";; type_of_goal();; searchn 1 [`norm z = &0`] "COMPLEX_NORM_ZERO" searchn 1 [`real`;`Re`]"REAL_NORM";; searcht 5 [`(a = b) = (b = a)`];; searcht 5 [`Cx (Re (t))`];; searcht 5 [`Arg (Cx (&0))`];; searcht 5 [`Arg x = Arg y`];; searcht 5 [`Arg`;`Re`];; searcht 5 [`inv (x/(y:complex))`];; searcht 15 [`Arg`;`real`];; help "LAND_CONV";; searchn 6 [`Arg (x)`;`pi`] "ARG_INV";; type_of_goal();; type_of `azim`;; type_of `plane`;; (* GEOM_BASIS_MULTIPLE_TAC 3`v:real^3` *) (* add_linear_invariants [FCHANGED_LINEAR_INVARIANT ; LINEAR_0;RCONE_LINEAR_INVARIANT ];; *) (* let backup_invariant_under_linear = !invariant_under_linear;; *) (* let restore _ = invariant_under_linear := backup_invariant_under_linear;; restore();; *) (* add_linear_invariants [SOLVEC0_LINEAR_INVARIANT_3];; *) (* searcht 15 [`facet_rep_a`];; POLY_SORT_BIJ;; searcht 15 [`plane`];; *) (* let _ = [`ball`;`half_spaces`;`weakly_saturated`;`lmfun_ineq_center`];; let _ = [ball;Tarjjuw.half_spaces;Tarjjuw.weakly_saturated;Pack_defs.lmfun_ineq_center];; let _ = [Tarjjuw.TARJJUW;Ysskqoy.YSSKQOY];; *) (* TARJJUW *) (* searcht 5 [`packing`;`FINITE`];; searcht 15 [`ball_annulus`];; searcht 5 [`sup`;`FINITE`];; weakly_saturated;; ball_annulus;; searcht 5 [`weakly_saturated`];; type_of `ball_annulus`;; def_of_regexp "ball_annulus";; constant_of_regexp "ball_annulus";; def_of_regexp "ball_annul";; Tarjjuw.TARJJUW;; search [name "TARJ"];; apropos();; constant_of_regexp "TRI";; def_of_regexp "sol$";; def_of_regexp "solid_triangle";; help "apropos_searching";; constant_of_regexp "satur";; ["weakly_saturated"; "saturated"];; def_of_regexp "weakly_saturated";; def_of_regexp "max";; constant_of_regexp "inter";; def_of_regexp "closed_real_interval";; search [`weakly_saturated`];; (* "Tarjjuw.TARJJUW" *) Tarjjuw.TARJJUW;; def_of_regexp "ball";; (* open *) def_of_regexp "half_spaces";; def_of_regexp "ineq_cen";; searcht 5 [`weakly_saturated`];; let ineq693 = `~lmfun_ineq_center V`;; type_of `sum`;; searcht 5 [`..`];; type_of `lmfun`;; searcht 5 [`lmfn_ineq_center`];; *) searcht 5 [`pad2d3d`;`dot`];; (* Tue Feb 28 08:27:45 EST 2012 *) searcht 50 [`facet_of`;`polyhedron`;`IN`;`t % v`];; mark 0;; searcht 20 [`rcone_gt`;`vec`];; searcht 20 [`rconesgn`];; mark 6;; mark 7;; searcht 20 [`x - vec 0`];; mark 0;; searcht 5 [`dist (x, vec 0)`];; mark 0;; searcht 5 [`(a % v) dot u`];; mark 0;; searcht 5 [`norm (a % v)`];; mark 0;; searcht 5 [`norm`; `v dot v`];; mark 4;; searcht 15 [`(a:real) * c < b * d`];; searcht 15 [`abs x = x`];; mark 12;; searcht 15[`&0 < a / b`];; mark 1;; mark 6;; searcht 15 [`x * y < x * v`];; mark 4;; searcht 15[`&0 < a * b`];; mark 4;; searcht 15 [`polyhedron`;`face_of`;`a % v`];; searcht 15 [name "INTERI";name "POLY"];; mark 0;; searcht 100 [`relative_interior`;`polyhedron`];; mark 0;; FACET_OF_POLYHEDRON_EXPLICIT;; searcht 50 [`polyhedron`;`fchanged`];; searcht 5 [`x /\ y <=> ((u:A->bool) = b)`];; searcht 5 [`x SUBSET y /\ y SUBSET x`];; searcht 5 [`x SUBSET a INTER b`];; searcht 5[`relative_interior f SUBSET fchanged f`];; mark 0;; searcht 5 [`x SUBSET affine hull x`];; mark 0;; searcht 5 [`relative_interior s SUBSET s`];; mark 0;; searcht 10 [`fchanged`];; searcht 10 [`a % v`;` affine hull f`];; mark 3;; searcht 10 [`a % v = b % v`];; mark 0;; searcht 10 [`affine`;`vec 0`];; mark 2;; searcht 10 [`dependent`];; searcht 5 [`a % vec 0`];; searcht 5 [`a - vec 0`];; searcht 5 [`vec 0 + u`];; searcht 5 [`vec 0 - u`];; searcht 5 [`u IN (:A)`];; VECTOR_ARITH;; searcht 5 [` t % u = vec 0`];; mark 2;; searcht 5[`face_of`;`affine`];; (* Sun Mar 4 10:27:12 EST 2012, counting spheres *) searcht 15 [`relative_interior`;`face_of`];; mark 1;; searcht 10 [`face_of`;`hull`];; mark 2;; searcht 10 [`~(X = {})`];; searcht 10 [`relative_interior f SUBSET y`];; mark 0;; searcht 10 [`affine hull A SUBSET affine hull B`];; mark 0;; searcht 10 [`&1 % v`];; mark 0;; searcht 10 [`u hull A SUBSET u hull B`];; mark 3;; searcht 5 [`u hull (u hull A)`];; mark 1;; searcht 5 [`u IN {a,b}`];; research 5;; searcht 5 [`f SUBSET P hull x`];; mark 0;; searcht 5 [`convex`; `polyhedron`];; mark 0;; searcht 5 [`face_of`;`facet_of`];; mark 1;; searcht 5 [`relative_interior`;`interior`];; mark 0;; searcht 15 [`facet_of`];; searcht 5 [`relative_interior x SUBSET y`];; mark 0;; FCHANGED_AFFINE;; searcht 5 [name "POLY"; name "COLL"; name "FACE"];; searcht 5 [`affine hull c`;`facet_of`];; mark 1;; searcht 5 [`affine hull u = (:real^N)`];; mark 3;; searcht 5 [`x dot y = y dot x`];; mark 0;; searcht 5 [`v dot (a % w)`];; searcht 5 [`rcone_gt`];; searcht 15 [`rconesgn`];; searcht 15 [`dist(v,vec 0)`];; searcht 15 [`a < b`;`a pow 2 < b pow 2`];; mark 3;; searcht 5 [`(a * b) pow 2`];; mark 1;; searcht 5 [`norm p pow 2`];; mark 1;; mark 2;; searcht 5 [`&0 <= a * b`];; mark 4;; searcht 5 [`&0 <= norm x`];; mark 0;; searcht 15 [`a < b`;`a pow 2 < b pow 2`];; mark 2;; searcht 5 [`dist (a,b) pow 2`];; mark 0;; searcht 20 [`sqrt(&1 - a pow 2)`];; searcht 5 [`norm v = &0`];; mark 3;; searcht 5 [`sqrt x pow 2`];; mark 1;; searcht 5 [`&0 <= &1 - t pow 2`];; mark 0;; searcht 15 [`a * x < b * x`];; mark 2;; searcht 5 [`&0 < a * b`];; mark 4;; searcht 5 [`&0 < t pow 2`];; mark 0;; searcht 5 [`cos (arcV a b c)`];; mark 0;; searcht 5 [`&0 < a * b`];; mark 4;; mark 3;; searcht 5 [`&0 < &1 - t pow 2`];; searcht 5 [`t pow 2 < &1`];; mark 0;; searcht 5 [`&0 < sqrt u`];; mark 1;; searcht 5 [`&0 < norm v`];; mark 0;; searcht 5 [`a*b = a * c`];; mark 0;; searcht 5 [`a % v = vec 0`];; mark 2;; searcht 5 [`a / b = &0`];; mark 2;; searcht 5 [`vec 0 dot u = &0`];; mark 0;; searcht 5 [`(a/b) pow 2`];; mark 0;; searcht 5 [`x pow 2 = y pow 2`];; mark 4;; searcht 5 [`a dot b = b dot a`];; mark 0;; searchk 5 [`&0 <= a/b`];; mark 1;; searcht 5 [`&0 <= a * b`];; mark 4;; searcht 5 [`&0 <= norm t`];; mark 0;; searcht 5 [`v dot v = &0`];; mark 0;; searcht 5 [`norm x = &0`];; mark 3;; searchk 5 [`norm x pow 2`];; searchk 5 [`measure A <= measure ( B)`];; mark 0;; searcht 5 [`measurable`;`wedge`];; mark 0;; searcht 5 [`eventually_radial`;`wedge`];; searcht 14 [`eventually_radial`];; mark 7;; vol_solid_triangle_ortho;; searcht 5 [`vol_solid_triangle`;`solid_triangle`];; mark 1;; searcht 3 [`solid_triangle`];; mark 0;; searcht 5 [`cone0`];; mark 1;; searcht 5 [`measure`;`measurable`];; searchk 5 [`primitive`];; (* measurability of solid_triangle *) mark 0;; mark 1;; searchk 50 [`fchanged`;`topological_component_yfan`];; mark 1;; searcht 50 [`topological_component_yfan`;`measurable`];; mark 0;; searcht 50 [`FAN`;`polyhedron`];; mark 0;; searcht 50 [name "PIIJ"];; mark 0;; searcht 5 [`fan80`];; mark 0;; searcht 5 [`set_of_edge`;`polyhedron`];; mark 1;; searcht 5 [`eventually_radial`;`topological_component_yfan`];; searchk 5 [`radial`];; mark 5;; searchk 5 [`normball`;`ball`];; mark 1;; searchk 5 [`fchanged`;`t % v`];; mark 0;; searchk 5 [`a % b % c`];; mark 0;; searchk 5 [`&0 < a * b`];; searcht 5 [`radial`;`ball`];; searcht 5 [`IN`;`ball`];; mark 3;; searcht 5 [`dist`;`norm`];; mark 1;; searchk 5 [`norm (--u)`];; mark 0;; searchk 5 [`norm (t % u)`];; searchk 10 [`wedge`;`azim`];; mark 5;; searcht 5 [`azim`;`azim a b c d + azim a b d e`];; searcht 5 [`X = {}`;`?`];; mark 2;; searchk 5 [name "SHIFT";`azim`];; mark 0;; searchk 5 [`azim a b c c `];; mark 0;; searchk 5 [`aff_gt`];; mark 1;; searchk 5 [`cone0`];; searcht 15 [`affsign`;`SUBSET`];; searchk 5 [`affsign`];; mark 32;; searcht 15 [`aff_gt`;`convex`];; mark 0;; searcht 15 [`convex`;`fchanged`];; searcht 5 [`convex`;`topological_component_yfan`];; searcht 15 [`fchanged`;`aff_gt`];; searcht 15[ `fchanged`;`affsign`];; searchk 5 [`cone0`];; searchk 5 [`fchanged`];; searchk 5 [`convex0`];; search [`affsign`];; AFFSIGN;; searcht 5 [`{} UNION X`];; mark 0;; searchk 5 [`x IN {}`];; mark 0;; searchk 8 [`vsum`;`INSERT`];; mark 4;; mark 6;; searchk 5 [`collinear`;`~(x = y)`];; mark 0;; searcht 15 [`collinear {x,y,z} = collinear {u,v,w}`];; 1;; (* Tue Mar 6 06:09:41 EST 2012 *) searcht 15 [`face_of`;`SUBSET`;`convex`];; mark 8;; searchk 5 [`sum`;`INSERT`];; mark 7;; mark 2;; searcht 15 [`convex`;`sum`];; (*117*) mark 9;; searchk 5 [`relative_interior a SUBSET relative_interior b`];; mark 0;; searcht 15 [`convex`;`facet_of`];; mark 4;; searchk 5 [`convex`;`face_of`];; (* ?120 *) mark 2;; searcht 5 [`sgn_gt`];; mark 3;; searcht 15 [`a <= sum s f `];; mark 6;; searcht 5 [`sum (A UNION B) f `];; mark 0;; searcht 5 [`x HAS_SIZE n`;`x IN u`];; searcht 5 [`x HAS_SIZE 0`];; mark 0;; searcht 5 [`x HAS_SIZE 1`;`x IN u`];; mark 0;; searchk 5 [`sum s f <= sum s' f`];; mark 0;; searchk 15 [`CARD`;`INSERT`];; searchk 15 [`convex hull a SUBSET f`];; (* 128 *) mark 3;; searchk 15 [`convex hull s = s`];; (* 129 *) mark 2;; searchk 15 [`convex`;`facet_of`];; searchk 5 [`face_of`;`facet_of`];; searchk 15 [`affine hull u`;`aff_dim`];; mark 5;; searchk 15 [`convex hull u `;`aff_dim`];; searchk 15 [`aff_dim`;`facet_of`];; (* 42 *) searchk 15 [`interior`;`aff_dim`];; mark 0;; searchk 15 [`collinear`;`aff_dim`];; searchk 5 [`SUBSET`;`aff_dim`];; (* 132 *) mark 0;; searchk 5 [`x SUBSET P hull x`];; searchk 15 [`aff_dim`;`INSERT`];; mark 3;; mark 2;; searchk 5 [`affine`;`collinear`];; mark 2;; searchk 5 [`affsign`;`{}`;`{x}`];; searchk 5 [`a % vsum s f`];; mark 0;; searchk 5 [`a % b % c`];; searchk 5 [`UNION`;`INSERT`];; mark 3;; searchk 15 [`sum`;`INSERT`];; mark 6;; searchk 15 [`a % vec 0 `];; mark 0;; searchk 5 [`sum s (\v. f v * u)` ];; mark 1;; searchk 5 [`x / y`;`inv`];; mark 1;; searchk 5 [`face_of`;`interior`];; mark 0;; searcht 15 [`a INTER b = {}`];; mark 14;; searchk 5 [`aff_dim (convex hull s)`];; mark 0;; searchk 5 [`x:real^3`;`?`;`u dot v = &0`;`~(v = vec 0)`];; searchk 5 [`eventually_radial`;`sol`];; searcht 50 [`sol`];; mark 8;; (* 145, sol def *) mark 15;; (* 146, SOL_UNIONS *) searchk 5 [`radial_norm`;`radial`];; mark 0;; (* 147 *) vol_solid_triangle_ortho;; searcht 15 [def "collinear"];; searchk 15 [`collinear`;`~(a = (b:real^N))`];; mark 11;; searchk 15 [`affine hull {x,y}`];; mark 10;; searchk 15 [`affine`;`aff`];; mark 5;; searchk 15 [`aff_gt`;`wedge`];; mark 2;; searchk 15 [`collinear {vec 0 ,a,b}`];; mark 13;; mark 4;; searchk 15 [`v dot v = &0`];; 1;; (* Wed Mar 7 07:03:30 EST 2012 *) searchk 5 [`&0 <= sqrt x`];; mark 2;; searchk 5 [`(\x. Q x) x = Q x`];; 1;; (*---^^ command line ^^ --- *) (* GG generic commands *) List.map (fun n -> List.nth !search_results n) (100--120);; suggest();; result 200 [];; mark 0;; type_of_goal();; write 0;; map (fun (_,s,_,_) -> s) !search_results;; let search_result_dump = ["REAL_LT_MUL"; "REAL_LT_LMUL"; "REAL_LT_DIV"; "Local_lemmas.REAL_LT_DIV_NEG"; "Trigonometry2.LT_IMP_ABS_REFL"; "NORM_POW_2"; "NORM_MUL"; "DOT_LMUL"; "DIST_0"; "VECTOR_SUB_RZERO"; "rconesgn"; "rcone_gt"; "Polyhedron.REDUCE_POINT_FACET_EXISTS"; "POLYHEDRON_COLLINEAR_FACES"; "DOT_POS_LT"; "DOT_RZERO"; "facet_of"; "DOT_LMUL"; "Trigonometry2.EXISTS_OTHOR_VECTOR_DIFFF_VEC0"; "Trigonometry2.EXISTS_UNIT_OTHOR_VECTOR"; "INJECTIVE_PAD2D3D"; "COMPLEX_VEC_0"; "COMPLEX_VEC_0"; "Counting_spheres.facet_rep_def"; "CX_INJ"; "COMPLEX_NORM_CX"; "POLYTOPE_EQ_BOUNDED_POLYHEDRON"; "POLYTOPE_IMP_CONVEX"; "POLYTOPE_IMP_COMPACT"; "EXTREME_POINT_EXISTS_CONVEX"; "FACE_OF_SING"; "FACE_OF_POLYHEDRON_SUBSET_FACET"; "POLYTOPE_FACET_EXISTS"];; let search_result_dump_march7_8am = ["Trigonometry2.COLLINEAR_TRANSABLE"; "Trigonometry2.COLLINEAR_TRANSABLE"; "Trigonometry2.COLLINEAR_TRANSABLE"; "Trigonometry2.COLLINEAR_TRANSABLE"; "COLLINEAR_LEMMA_ALT"; "WEDGE_LUNE_GT"; "COLLINEAR_3_AFFINE_HULL"; "Sphere.aff"; "AFFINE_HULL_2_ALT"; "Marchal_cells_2.RADIAL_VS_RADIAL_NORM"; "Conforming.SOL_UNIONS"; "Vol1.sol"; "AFF_DIM_CONVEX_HULL"; "Hypermap.lemma_in_disjoint"; "FACE_OF_DISJOINT_INTERIOR"; "real_div"; "SUM_RMUL"; "VECTOR_MUL_RZERO"; "SUM_CLAUSES"; "Packing3.SING_UNION_EQ_INSERT"; "VSUM_LMUL"; "Collect_geom.IN_AFFINE_HULL_IMP_COLLINEAR"; "AFF_DIM_2"; "AFF_DIM_INSERT"; "AFF_DIM_SUBSET"; "Polyhedron.AFF_DIM_INTERIOR_EQ_3"; "AFF_DIM_EQ_AFFINE_HULL"; "CONVEX_HULL_EQ"; "Marchal_cells.CONVEX_HULL_SUBSET"; "Upfzbzm_support_lemmas.SUM_SET_OF_2_ELEMENTS"; "SUM_SUBSET_SIMPLE"; "HAS_SIZE_1_EXISTS"; "HAS_SIZE_0"; "SUM_UNION"; "SUM_POS_LE"; "sgn_gt"; "FACE_OF_IMP_CONVEX"; "POLYTOPE_UNION_CONVEX_HULL_FACETS"; "SUBSET_RELATIVE_INTERIOR"; "EXPLICIT_SUBSET_RELATIVE_INTERIOR_CONVEX_HULL"; "Geomdetail.SUM_DIS3"; "face_of"; "FACE_OF_CONVEX_HULL_SUBSET"; "Geomdetail.VSUM_DIS3"; "Collect_geom.NOT_COLLINEAR_IMP_2_UNEQUAL"; "Marchal_cells_2.VSUM_CLAUSES_alt"; "NOT_IN_EMPTY"; "UNION_EMPTY"; "aff_gt_def"; "CONVEX_AFF_GT"; "affsign"; "Sphere.aff_gt_def"; "AZIM_REFL"; "AZIM_BASE_SHIFT_LT"; "Counting_spheres.EMPTY_NOT_EXISTS_IN"; "wedge"; "NORM_NEG"; "dist"; "IN_BALL"; "VECTOR_MUL_ASSOC"; "Polyhedron.fchanged"; "NORMBALL_BALL"; "Sphere.radial"; "Polyhedron.CARD_SET_OF_EDGE_INEQ_1_POLYHEDRON"; "Polyhedron.POLYTOPE_FAN80"; "Conforming.PIIJBJK"; "Polyhedron.POLYHEDRON_FAN"; "Conforming.MEASURABLE_TOPOLOGICAL_COMPONENT_YFAN_INTER_BALL"; "Polyhedron.FCHANGED_IN_COMPONENT"; "primitive"; "MEASURABLE_RULES"; "Sphere.cone0"; "solid_triangle"; "Vol1.volume_prop_fix"; "Sphere.eventually_radial"; "MEASURABLE_BALL_WEDGE"; "MEASURE_SUBSET"; "NORM_EQ_0"; "DOT_EQ_0"; "NORM_POS_LE"; "Real_ext.REAL_PROP_NN_MUL2"; "Calc_derivative.invert_den_le"; "DOT_SYM"; "Collect_geom.EQ_POW2_COND"; "Trigonometry2.DIV_POW2"; "DOT_LZERO"; "Calc_derivative.invert_den_eq"; "VECTOR_MUL_EQ_0"; "REAL_EQ_MUL_LCANCEL"; "NORM_POS_LT"; "SQRT_POS_LT"; "ABS_SQUARE_LT_1"; "Calc_derivative.invert_den_lt"; "REAL_LT_MUL"; "Trigonometry1.DOT_COS"; "Trigonometry2.NOT_ZERO_EQ_POW2_LT"; "REAL_LT_MUL"; "REAL_LT_RMUL"; "Trigonometry2.UNIT_BOUNDED_IN_TOW_FORMS"; "SQRT_POW_2"; "NORM_EQ_0"; "Collect_geom.DIST_POW2_DOT"; "Tarjjuw.CHANGE_TARJJUW_4"; "NORM_POS_LE"; "Real_ext.REAL_PROP_NN_MUL2"; "NORM_POW_2"; "DOT_SQUARE_NORM"; "Trigonometry2.MUL_POW2"; "Tactics_jordan.REAL_POW_2_LT"; "DOT_SYM"; "Polyhedron.INTERIOR_AFFINIE_HUL_EQ_UNIV"; "Counting_spheres.affine_facet_hyper"; "RELATIVE_INTERIOR_SUBSET"; "INTERIOR_SUBSET_RELATIVE_INTERIOR"; "facet_of"; "POLYHEDRON_IMP_CONVEX"; "Ldurdpn.SUBSET_P_HULL"; "HULL_HULL"; "HULL_MONO"; "VECTOR_MUL_LID"; "Marchal_cells_2.AFFINE_SUBSET_KY_LEMMA"; "RELATIVE_INTERIOR_SUBSET"; "FACE_OF_STILLCONVEX"; "FACE_OF_DISJOINT_RELATIVE_INTERIOR"; "REAL_LT_MUL"; "REAL_LT_LMUL"; "REAL_LT_DIV"; "Local_lemmas.REAL_LT_DIV_NEG"; "Trigonometry2.LT_IMP_ABS_REFL"; "NORM_POW_2"; "NORM_MUL"; "DOT_LMUL"; "DIST_0"; "VECTOR_SUB_RZERO"; "rconesgn"; "rcone_gt"; "Polyhedron.REDUCE_POINT_FACET_EXISTS"; "POLYHEDRON_COLLINEAR_FACES"; "DOT_POS_LT"; "DOT_RZERO"; "facet_of"; "DOT_LMUL"; "Trigonometry2.EXISTS_OTHOR_VECTOR_DIFFF_VEC0"; "Trigonometry2.EXISTS_UNIT_OTHOR_VECTOR"; "INJECTIVE_PAD2D3D"; "COMPLEX_VEC_0"; "COMPLEX_VEC_0"; "Counting_spheres.facet_rep_def"; "CX_INJ"; "COMPLEX_NORM_CX"; "POLYTOPE_EQ_BOUNDED_POLYHEDRON"; "POLYTOPE_IMP_CONVEX"; "POLYTOPE_IMP_COMPACT"; "EXTREME_POINT_EXISTS_CONVEX"; "FACE_OF_SING"; "FACE_OF_POLYHEDRON_SUBSET_FACET"; "POLYTOPE_FACET_EXISTS"];; search_results := [];; search_results := augment_search_results search_result_dump;; map retrieve_search_number (21--39);; (* Oct 24, 2012 searches for EUSOTYP2_general *) ALL_TAC;; searc '0' 2 [`azim a b c d = azim a' b' c' d'`];; searcht 5 [`DISJOINT`;`collinear`];; EQ_SYM;; (GSYM Topology.th1);;; CHOOSE_TAC;; VECTOR_ARITH;; azim_axis;; searc 'a' 3 [`~(?x. p)`;];; searc 'b' 2 [`bounded`;`SUBSET`];; searc 'c' 1 [`collinear`;`vec 0 `;`t % v`];; searc 'd' 3 [`~(a \/ b)`];; searc 'e' 0 [`(c % v) dot w`];; searc 'f' 0 [`face_of`;`facet_of`];; searc 'g' 0 [`(&0) % v`];; searc 'h' 3 [`i IN a..b`];; searc 'i' 3 [`&0 < a / b`];; searc 'j' 0 [`x % v = y % v`];; searc 'l' 0 [`(a + b) dot v`];; searc 'p' 0 [`polyhedron`;`face_of`;`==>`];; searc 's' 0 [`SUBSET`;`face_of`];; searc 't' 1 [`collinear {(vec 0),a,b}`;`t % x`];; searc 'u' 8 [`collinear`;`t % x`];; searc 'v' 0 [`a % b % c`];; searc 'w' 6 [`collinear`;`vec 0`];; searc 'x' 6 [`&0 < a * b`];; searc 'y' 0 [`arcV a b c = arcV a c b`];; searc 'z' 1 [`arcV`;`t % v`];; Print_types.print_goal_types();; searcht 5 [`(a - b) dot v`];; type_of `rcone`;; searcht 5[`&0 < u dot u`];; searcht 5 [`{x,x,y}`];; RDISK_R;; Counting_spheres.EUSOTYP_general;; searc '5' 2 [`x % y = (vec 0)`];; searcht 5 [`x IN (a INSERT b)`];; searc '4' 7 [`X INTER Y = {}`];; (* searc '2' 1 [`facet_of`;`face_of`];; searc '1' 3 [`{}`;`?`];; searc '0' 0 [`interior`;`face_of`];; *) (* WEDGE_LUNE_GT;; searc '0' 0 [`azim`;`dihV`];; *) (* Oct 28, 2012 *) let searcj c = searcht;; searc '3' 6 [`&0 < t2/t`];; searc '2' 0 [`t % u % v`];; searc '1' 16 [`<=>`;`==>`];; searcht 25 [`(?t. u) <=> (?t. y)`];; searc '0' 2 [`aff_gt {x} {u,v,w}`; `t % v`];; searcht 5 [`collinear`;`DISJOINT`];; searcht 5 [def "t0"];; type_of `t0`;; searcht 5 [`aff_gt`; `t % x`];; Print_types.print_thm_types CONE0_FCHANGED;; Print_types.print_goal_types();; searc '4' 0 [`t % (vec 0)`];; searc '5' 2 [`x = {}`;`?`];; searc '6' 2 [`collinear`;`coplanar`];; searc '7' 0 [`coplanar`;`~(a = (b:real^A))`];; searc '8' 0 [`coplanar`;`t % v`;`vec 0`];; searc '9' 0 [`x IN {y}`];; searc 'a' 0 [`x IN A INTER B`];; searc 'b' 0 [`coplanar`;`dihV`];; searc 'c' 1 [`&0 <= dihV a b c d`];; searc 'd' 6 [`SUBSET`;`INTER`];; searcht 5 [`wedge`;`aff_gt`];; searc 'i' 0 [`cone0`;`aff_gt`];; searc 'e' 0 [`x IN {}`];; searc '0' 2 [`a SUBSET b INTER c`];; searcht 5 [`measurable`;`cone0`];; searc 'f' 0 [`measurable`;`aff_gt`];; searc 'g' 1 [`ball`;`normball`];; searc 'h' 0 [`A INTER B = B INTER A`];; searc 'i' 0 [`cone0`;`aff_gt`];; searcht 5 [`measurable (A INTER B)`];; searc 'j' 2 [`radial_norm`;`aff_gt`];; searcht 5 [`solid_triangle`;`cone0`];; searcht 5 [`vol`;`sol`];; searcht 5 [`vol`;`vol_solid_triangle`];; CONJUNCT2 Vol1.volume_props;; help "CONJUNCT2";; searc 'k' 0 [`azim`;`dihV`];; searcht 5 [`&0 < pi`];; searc 'l' 2 [`wedge`;`aff_gt`];; searc 'm' 0 [`measurable (X UNION Y)`];; searcht 5 [`(A UNION B) INTER C`];; UNION_OVER_INTER;; searc 'n' 0 [`radial_norm`;`UNION`];; searc 'p' 1 [`radial_norm`;`UNION`];; searc 'q' 1 [`dihV a b c d = dihV a b d c`];; searc 'r' 2 [`wedge`;`aff_gt`];; searcht 15 [`aff_gt {x,x'} y SUBSET aff_gt {x,x'} z`];; searcht 15 [`x IN wedge a b c d`];; searc 's' 5 [`wedge`;`azim`];; searc 't' 1 [`fchanged c = x`];; searcht 5 [`relative_interior x SUBSET y`];; searc 'u' 0 [`a % v dot w`];; searcht 5 [`x*b = b`];; searc 'v' 0 [`sol`;`vol`];; searc 'w' 8 [`measure`;`sum`];; type_of `measure`;; `measure:(real^3->bool)->real`;; GOTCJAH_convex_sum;; (* Oct 29, 2012 *) searc 'a' 0 [`collinear {(vec 0),v,u}`;`t % v`];; Trigonometry2.EXISTS_OTHOR_VECTOR_DIFFF_VEC0;; searc 'b' 1 [`~(?t. p)`];; searc 'c' 2 [`t % v = vec 0`];; searc 'd' 3 [`azim a b c d + azim a b d e `];; searc 'e' 0 [`measurable {}`];; searc 'f' 0 [`radial_norm a b {}`];; help_grep "CAS.*TAC";; searc 'g' 0 [`{} INTER B`];; searc 'h' 0 [`sol u {}`];; searc 'i' 0 [`sin(&0)`];; searc 'j' 0 [`asn(&0)`];; SKOLEM_THM;; searc 'k' 3 [`measure`;`has_measure`];; searc 'l' 0]\[`measure`;`SUBSET`];; GOTCJAH_convex_sum;; WEDGE_ORDER_DISJOINT;; ORDER_AZIM_SUM2Pi;; searcht 5 [`sum`;`a..b`;`f o c`];; searc 'm' 2 [`sum (a..b) f = sum (c..d) g`];; searc 'n' 1 [`a < (b:num)`;`a < b`];; searc 'o' 4 [`&0 <= a * b`];; searc 'p' 0 [`a <= (b:num)`;`a <= b`];; searc 'q' 1 [`&0 <= azim a b c d`];; searc 'r' 2 [`sum f x = sum f y`];; searc 's' 0 [`sum f (\i. t * r i)`];; searc 't' 0 [`sol`;`vol`];; searc 'u' 1 [`(UNIONS X) INTER Y`];; searc 'v' 4 [`measurable (UNIONS s)`];; searcht 5 [`radial_norm`;`UNIONS`];; SOL_UNIONS;; searc 'w' 0 [`radial_norm`;`DIFF`];; searc 'x' 0 [`sol`;`UNION`];; searcht 5 [`sol`;`DIFF`];; searcht 5 [`sol x y <= sol x z`];; searc 'y' 1 [`sol`;`UNIONS`];; searc 'z' 0 [`FINITE (IMAGE X u)`];; searc 'a' 0 [`FINITE (a..b)`];; searc 'b' 2 [`sum (IMAGE X y)`];; searc 'c' 3 [`sum (IMAGE X y)`];; searcht 35 [`(\i. f i = \j. g j) <=> `];; EXT_AXIOM;; FUN_EQ_THM;; searcht 5 [`sol`;`SUBSET`];; searcht 5 [`sol x y <= sol x z`];; searc 'd' 0 [`measurable`;`DIFF`];; searc 'e' 0 [`radial_norm`;`DIFF`];; searcht 5 [`(t DIFF s) INTER u`];; searcht 5 [`sol x y >= &0`];; searc 'h' 0 [`&0 <= measure u`];; searc 'f' 4 [`&0 <= x / y`];; searc 'g' 4 [`&0 <= x * y`];; searc 'i' 11 [`&0 <= x pow n`];; searc 'j' 0 [`radial_norm`;`UNIONS`];; searcht 15 [`FINITE { f s | g s }`];; searc 'k' 0 [`measurable`;`fchanged`];; FCHANGED_RADIAL;; searc 'l' 0 [`radial`;`radial_norm`];; (* Oct 31, 2012 *) searcht 5 [`v IN rcone_gt x y z`];; searcht 15 [`rcone_gt x y z`];; searc 'a' 0 [`dist(v, vec 0)`;`norm`];; searcht 5 [`norm v = &0`];; searc 'b' 4 [`norm`;`dot`];; searc 'c' 5 [`&0 < a * b`];; searc 'd' 0 [`&0 < norm x`];; searc 'e' 0 [`norm x = &0`];; searc 'f' 0 [`vec 0 dot v`];; searc 'g' 0 [`v dot vec 0`];; searc 'h' 0 [`a % v dot u`];; searcht 2 [`arcV`;`rcone_gt`];; searc 'i' 0 [`cos`;`a dot b`];; Print_types.print_thm_types Trigonometry1.DOT_COS;; searcht 5 [`&0 < cos x`];; searc 'j' 1 [`cos x < cos y`];; searc 'k' 0 [`&0 <= arcV a b c`];; searc 'p' 2 [`x * y < x * z`];; searc 'q' 0 [`arcV x y z + arcV x y' z'`];; searc 'r' 1 [`&0 < cos x`];; searc 's' 0 [`cos x <= &1`];; searc 't' 4 [`cos x = &1`];; searc 'u' 2 [`~(?x. p)`];; searc 'v' 1 [`~(a /\ b) = c`];; searc 'w' 4 [`a <= b`;`&a <= &b`];; searc 'x' 4 [`&0 <= x * y`];; searcht 5 [`&0 <= arcV x y z`];; searc 'y' 0 [`arcV x y z = arcV x z y`];; searc 'z' 12 [`&0 < x * y`];; searcht 5 [`x * y <= &0`];; (* START WITH THIS ONE. Nov 1. *) searc 'a' 0 [name "WBLARHH"];; searc 'b' 0 [name "AMH"];; (* need to relat facet_of^2 to edges,edge_of *) searc 'c' 0 [`edges`;`edge_of`];; searc 'd' 0 [`edge_of`;`face_of`];; (* def of edge_of=face_of aff_dim 1 *) searc 'e' 0 [`conforming`];; (* def of conforming *) searcht 5 [name "CFYXF"];; (* 0 relates edges<=> EDGES0_FAN *) searcht 5 [def "edge_of"];; searcht 5 [`fully_surrounded`];; searcht 5 [`plain_hypermap`];; searcht 5 [def "plain"];; searcht 50 [`FAN`];; (* Nov 1, 2012 *) searcht 5 [`edges`;`face_of`];; searcht 5 [`hypermap_of_fan`;`hypermap1_of_fanx`];; searcht 50 [`hypermap_of_fan`];; searcht 50 [`hypermap1_of_fanx`];; searcht 5 [`facet_of`;`aff_dim`];; searc 'a' 1 [`x = y`;`x ==> y`;`x /\ y`];; searc 'b' 2 [`face_of`;`facet_of`];; searcht 'f' 18 [`face_of`];; searc 'c' 3 [`aff_dim`;`{}`];; type_of `aff_dim`;; searc 'd' 0 [`aff_dim`;`interior`;`3`];; searc 'e' 0 [`aff_dim`;`interior`;`2`];; searc 'f' 18 [`face_of`];; searc 'g' 1 [`face_of`;`SUBSET`];; searcht 5 [`facet_of`;`aff_dim`];; searc 'h' 0 [`edges`;`segment`];; BIJ_SYM;; searc 'i' 0 [`r (BIJ f U V) (BIJ g V U)`];; searcht 15 [`BIJ`;`(a,b)`];; searcht 5 [def "preimage"];; searcht 5 [`preimage`;`BIJ`];; searcht 5 [`IMAGE`;`BIJ`];; type_of `preimage`;; searc 'j' 0 [`( p ==> (?x. q x)) <=> (?x. p ==> q x)`];; SKOLEM_THM;; searcht 35 [`BIJ`];; searcht 5 [`BIJ`;`x ==> (u = v)`;`?`];; searcht 5 [def "BIJ"];; searcht 10 [def "INJ"];; searc 'k' 0 [`preimage`];; searcht 5 [`IMAGE f X SUBSET Y`];; INST_TYPE;; Print_types.print_goal_types();; searcht 5 [`FST (x,y)`];; searc 'l' 1 [`preimage`];; searcht 5 [def "hypermap1_of_fanx"];; searc 'm' 0 [`hypermap1_of_fanx`;`hypermap`;`e_fan`];; searc 'n' 1 [`face_set`];; Hypermap.dart;; searcht 5 [`tuple_hypermap`;`hypermap`];; searcht 50 [`hypermap_of_fan`;`hypermap`];; searcht 5 [`hypermap1_of_fanx`;`hypermap`];; searcht 15 [`HYP`];; searcht 15 [`d1_fan`];; searcht 5 [`{a,b} = {a',b'}`];; lemmaTGJISOK;; searcht 50 [`FAN`;`azim`];; searc 'a' 0 [`conforming`];; (* def *) searcht 50 [`conforming`];; searcht 50 [`conforming_fan`];; searc 'c' 0 [name "PIIJ"];; searc 'b' 2 [`fully_surrounded`];; (* dart_of_fan azim_dart *) searcht 5 [`azim_dart`];; (* azim_dart -> azim_fan *) searcht 5 [`azim_fan`];; (* sigma_fan *) searcht 5 [`FAN`;`sigma_fan`];; List.length (searcht 1000 [`FAN`]);; searcht 500 [`conforming`];; searc 'a' 0 [name "BSXA"];; searc 'b' 0 [`FAN`;`vertices`];; (* POLYHEDRON_FAN *) searc 'd' 0 [`fan80`;`polyhedron`];; searc 'e' 1 [`polyhedron`;`set_of_edge`];; searcht 5 [`polyhedron`;`conforming_fan`];; searcht 30 [`hypermap1_of_fanx`;`conforming_fan`];; searc 'f' 5 [`CARD`;`simple_hypermap`];; (* conditions for 3 <= CARD face *) searc 'g' 0 [name "TGJ"];; searc 'h' 0 [name "WGV"];; searc 'i' 0 [`plain_hypermap`;`FAN`];; searcht 5 [`plain_hypermap`;`FAN`];; Fan.plain_hypermap_fan;; Fan.e_fan_no_fix_point;; searcht 5 [`edge_map`;`e_fan`];; Fan.hypermap_of_fan_rep;; Hypermap.is_restricted;; searcht 5 [`d1_fan`;`d_fan`];; searcht 5 [`FAN`;`d20_fan`];; searc 'j' 7 [`d1_fan`;`d_fan`];; Print_types.print_goal_types();; searc 'k' 4 [`res`; `e_fan`];; searcht 5 [`p e_fan x = e_fan x`];; searc 'l' 0 [`x IN d1_fan u`;`res`];; (* not IN *) searc 'm' 2 [`x IN d1_fan u`;`res`];; help_grep "GEN";; GEN_ALL;; (GEN_ALL Fan.into_domain_e_fan);; Fan.plain_hypermap_fan;; searc 'm' 2 [`x IN d1_fan u`;`res`];; searcht 5 [`is_no_double_joins`];; Fan.face_subset_dart_fan;; (* each face is subset of d_fan *) Fan.FACE_FAN_NOT_EMPTY;; searc 'n' 4 [`3`;`CARD (face H x)`];; (* for hypermap_of_fan *) searc 'o' 0 [`planar_hypermap`;`FAN`];; searc 'p' 2 [`dart`;`hypermap1_of_fanx`];; searcht 3 [`dart`;`hypermap1_of_fanx`];; searc 'q' 0 [name "e_fan_no_fix"];; searcht 5 [`edge_map`;`e_fan`];; searcht 5 [`fan80`];; searcht 5 [`hypermap_of_fan`];; searcht 50 [`node`;`3`];; SURROUNDED_IMP_CARD_NODE_GE_3;; searcht 50 [`node_set`;`hypermap1_of_fanx`];; Conforming.SUM_AZIM_FAN_OF_NODE_EQ_2PI_I_FAN;; searcht 5 [`fan80`;`azim`];; searcht 5 [`n_fan`;`sigma_fan`];; searcht 5 [def "d1_fan"];; searcht 5 [def "dart_of_fan"];; searcht 5 [def "n_fan_pair"];; searcht 100 [`sigma_fan`;`CARD`];; searc 'r' 0 [`azim_fan`;`pi`;`sum`];; (* sum over node set azim_fan is 2pi *) searcht 5 [def"node_set"];; searc 'u' 0 [`node`;`node_set`];; searc 's' 0 [`fan80`;`polyhedron`];; searc 't' 0 [`polyhedron`;`azim_fan`];; searcht 5 [`sum f x < sum f y`];; searc 'v' 0 [`FINITE`;`node`];; searcht 5 [`node`;`{}`;omit `INSERT`];; searc 'w' 0 [`x IN node f x`];; searc 'x' 14 [`~(x = {})`];; searc 'y' 0 [`node f x SUBSET dart g`];; searc 'z' 1 [`sum`;`CARD`];; searc '0' 3 [`a * x <= b * x`];; searc '1' 4 [`&x <= &y`];; searcht 5 [def "edge_set"];; searcht 25 [`simple_hypermap`];; (* Nov 3, 2012 *) searcht 5 [`BIJ`;`o`];; searc 'a' 3 [`pr2`;`d_fan`];; (* injectivity of pr2,pr3 *) searc 'b' 2 [`{x,y} = {x',y'}`];; searc 'c' 7 [`e_fan`];; searcht 5 [def "e_fan"];; let nil = 0;; searcht nil [`e_fan`;`e_fan_pair`];; searcht 5 [`?`;`x = (a,b)`];; searcht 5 [`pr2`];; searc 'd' 0 [`dart`;`d_fan`];; searc 'e' 1 [`r e_fan x = e_fan y V E x`];; searc 'h' 0 [`(x,y) = (x',y')`];; searc 'f'0 [`d_fan`;`dart`];; searc 'g' 8 [`d_fan`;`d1_fan`];; EDGE_PAIR_pr23;; searc 'h' 10 [`e_fan`;`d1_fan`];; searc 'n' 14 [`simple_hypermap`];; searc 'i' 1 [`node_map H o face_map H`];; searcht 50 [`node_map H ( face_map H t)`];; searc 'k' 3 [`inverse f y = z`];; searc 'l' 0 [`(x = y) <=> (y = x)`];; searc 'm' 0 [`edge_map H permutes s`];; searc 'o' 0 [`node_map H y IN dart H`];; searc 'p' 0 [`y IN node H y`];; searcht 5 [`node_map H y IN node H y`];; searc 'q' 1 [`x IN node H y`];; searc 'r' 0 [`x POWER 1`];; searcht 5 [`face H (f x)`];; searc 's' 0 [`face H x = face H y`];; searc 't' 2 [`x IN face H y`];; searcht 15 [`x IN face H y`];; searcht 15 [`face H x = face H y`];; searcht 8 [`POWER`;`node`];; searc 'u' 16 [`(f POWER n) x = x`;`f x = x`];; searc 'v' 0 [`orbit_map`;`node`];; searc 'w' 0 [`f POWER 0`];; searc 'x' 1 [`CARD {x}`];; POLYHEDRON_CONFORMING_FAN;; searc 'y' 0 [`simple_hypermap`;`conforming_fan`];; searc 'a' 0 [`polyhedron`;`FAN`];; searc 'b' 0 [name "POLYHEDRON_NODE_3"];; searcht 5 [`d_fan`;`f1_fan`];; searc 'c' 0 [`d_fan`;`dart`];; searc 'd' 0 [`face_map H x IN dart H`];; searc 'e' 2 [`face_set H`;`dart`];; searcht 5 [`set_of_orbits`;`SUBSET`];; searc 'f' 0 [`face`;`dart`];; searc 'g' 6 [`y IN face H x`];; searc 'h' 0 [`y IN face H x`];; searcht 5 [name "D1_D"];; searc 'i' 0 [`set_of_edge`;`CARD`;`1`];; searcht 5 [name "WBL"];; searcht 5 [name "AMH"];; Cfyxfty.WBLARHH_BIJ;; Polyhedron.AMHFNXP_BIJ;; type_of `(topological_component_yfan (vec 0,vertices p,edges p))`;; searcht 5 [name "WGV"];; searc 'j' 0 [`edges`;`segment`];; searcht 5 [`edge_of`;`segment`];; searc 'k' 0 [`3`;`interior`;`aff_dim`];; searc 'l' 0 [`2`;`aff_dim`;`facet_of`];; searc 'm' 3 [`aff_dim`;`{}`];; searc 'n' 0 [`convex hull x`;`segment`];; searc 'o' 1 [`segment [a,b] = segment [c,d]`];; searc 'p' 0 [`{a,b} = {c,d}`];; searc 'q' 0 [`aff_dim`;`segment`];; searc 'r' 0 [`edge_of`;`aff_dim`];; searc 's' 1 [`polytope`;`polyhedron`];; searcht 5 [`face_of`;`facet_of`];; PREIMAGE_BIJ;; searcht 5 [`dartset_leads_into_fan`;`fchanged`];; Polyhedron.WBLARHH;; searc 't' 0 [`face H a IN face_set H`];; searc 'u' 4 [`?!`;`?`];; searc 'v' 1 [`preimage`];; searc 'w' 0 [`x IN {y}`];; searc 'x' 2 [`?`;`facet_of`];; searcht 5 [`s face_of s' ==> polyhedron s`;`polyhedron`];; searc 'y' 0 [`face_of`;`polytope`];; searc 'z' 12 [`facet_of`;`fchanged`];; searc 'a' 4 [`facet_of`;`fchanged`];; searc 'b' 0 [`x INTER x`];; searc 'c' 14 [`~(x = {})`];; searc 'd' 0 [`(x,y) = (x',y')`];; (* Nov 5, 2012 *) let searct _ = searcht;; searcht 5 [name "eq_sym"];; searcht 5 [`(x = y) <=> (y = x)`];; searc 'a' 0 [name "WBL"];; searc 'b' 2 [`?`;`?!`];; searc 'c' 0 [name "AMH"];; searc 'd' 1 [`preimage`];; searcht 5 [`face_set`;`face`];; searc 'e' 8 [`==>`;`<=>`];; searc 'f' 0 [`x IN face H x`];; Print_types.print_goal_types();; BIJ_FACET2_EDGE;; Print_types.print_thm_types BIJ_FACET2_EDGE;; type_of `edges c`;; BIJ_EDGES_DART_FACE;; (* Nov 6, 2012 *) searcht 15 [`sum f (\x. sum h g)`];; SUM_SUM_PRODUCT;; searc 'g' 0 [`CARD`;`sum`];; searc 'h' 8 [`(FINITE:((A#B)->bool)->bool)`];; searcht 5 [`SUBSET`;`FINITE`];; searc 'i' 0 [`face_of`;`facet_of`];; searc 'i' 0 [`face_of`;`facet_of`];; FACE_OF_TRANS;; help_grep "BETA_TAC";; searc 'j' 0 [`(\(a,b). f a b)`];; searc 'k' 0 [`FINITE`;`facet_of`];; searc 'l' 1 [`polytope`;`polyhedron`];; searc 'm' 0 [`face_of`;`FINITE`];; searc 'n' 2 [`sum f X = sum f Y`];; searcht 5 [`&x <= &y`;`(x:num) <= (y:num)`];; searcht 15 [name "REAL_OF_NUM"];; searcht 5 [`CARD {f,e | f facet_of P /\ e facet_of f}`];; searcht 5 [`6 * n - 12`];; searcht 5 [name "BIJ_FACET"];; POLYHEDRON_TGJISOK;; BIJ_DART_POLYEDGE;; searc 'o' 0 [`number_of_faces`];; searc 'p' 2 [`BIJ`;`CARD x= CARD y`];; searcht 5 [`rcone_gt`;`fchanged`];; searc 'q' 0 [`open`;`INTERS`];; searc 'r' 0 [`FINITE`;`IMAGE`];; searc 's' 0 [`FINITE`;`DIFF`];; searc 't' 0 [`open`;`a dot v < b`];; searc 'u' 1 [`open`;`ball`];; searcht 5 [`A INTER B SUBSET D INTER C`];; searc 'v' 3 [`affine hull x = x`];; searc 'w' 0 [`affine hull x SUBSET affine hull y`];; searc 'x' 0 [`affine`;`dot`];; searc 'y' 0 [`A INTER B SUBSET B`];; searcht 5 [`(A= B) ==> A SUBSET B `];; SET_CONV;; searcht 15 [`INTERS (IMAGE h f)`];; search [`relative_interior`;`<`];; Polyhedron.IN_RELATIVE_INTERIOR1;; RELATIVE_INTERIOR_POLYHEDRON_EXPLICIT;; (* via hyperplane ineqs *) FACET_OF_POLYHEDRON_EXPLICIT;; searc 'a' 0 [`( p ==> (?x. q x)) <=> (?x. p ==> q x)`];; searc 'b' 0 [`interior`;`affine`;`hull`];; searc 'c' 1 [`(UNIV) INTER A`];; searcht 5 [`INTERS A SUBSET INTERS B`];; DE_MORGAN_THM;; searc 'd' 2 [`~(?x. p)`];; (* Nov 8 *) Print_types.print_goal_types();; searc 'e' 0 [`x dot (vec 0) = &0`];; searc 'f' 0 [`a dot (t % p)`];; searc 'g' 2 [`x * z < y * z`];; searc 'h' 6 [`&0 < x/y`];; searc 'i' 0 [`&0 < norm p`];; searcht 5 [`dist`;`norm`];; searc 'j' 0 [`norm (t % p)`];; searc 'k' 3 [`norm p = &0`];; searcht 5 [`(a dot x < b) <=> (a' dot x < b')`];; searc 'l' 0 [`interior`;`a dot x <= b`];; searc 'm' 0 [`(x = y) <=> (y = x)`];; avoids;; searc 'n' 0 [`~(!x. p)`];; searcht 5 [`polyhedron`;`dot`;`<=`];; searcht 30 [name "TARJJ"];; Tarjjuw.TARJJUW;; searc 'o' 0 [`ball_annulus = y`];; searc 'p' 0 [`norm (vec 0) = &0`];; searc 'q' 6 [`&0 < x * y`];; searc 'r' 1 [`interior`;`ball`];; searc 's' 0 [`half_spaces`];; searc 't' 8 [`==>`;`<=>`];; FACET_OF_POLYHEDRON_EXPLICIT_ALT;; searc 'u' 0 [`v dot v = &0`];; searcht 5 [`v IN rcone_gt a v c`];; searc 'v' 1 [`fchanged`;`relative_interior`];; searc 'w' 0 [name "rcone_gt_facet"];; RELATIVE_INTERIOR_POLYHEDRON_EXPLICIT_ALT;; rcone_gt_facet;; FACET_OF_POLYHEDRON_EXPLICIT_ALT;; searc 'x' 0 [`x % y % z`];; searc 'y' 0 [`v % x = u % x`];; searcht 5 [`rcone_gt`;`dot`];; searc 'z' 0 [`&0 < &1 / x`];; searcht 5 [`&0 < x/ y `];; searc 'h' 6 [`&0 < x/y`];; rcone_gt_facet;; (* Nov 10, 2012 *) searc 'i' 0 [`lmfun_ineq_center`];; searc 'j' 0 [`ball_annulus`;`norm`];; searc 'k' 0 [`sum V x <= sum V y`];; searc 'l' 1 [`hl`];; searc 'm' 1 [`dist(vec 0,x)`];; searc 'n' 9 [`lmfun`];; searc 'o' 4 [`h0`];; searc 'p' 0 [`a / x <= b /x `];; searc 'q' 0 [`sum V (\v. &1)`];; searc 'r' 4 [`&x <= &y`];; searcht 5 [name "weak_sat"];; searc 's' 0 [`sum w x <= sum v x`];; searc 't' 0 [`&0 <= lmfun h`];; searc 'u' 0 [`sum`;`&4 * pi`];; searc 'v' 0 [`polyhedron`;`FAN`];; searc 'w' 0 [`conforming_fan`;`polyhedron`];; searcht 5 [`SURJ`;`sum`];; searc 'x' 0 [name "AMH"];; searc 'y' 1 [`sum`;`topological_component_yfan`];; searc 'z' 2 [`SURJ`;`IMAGE`];; searc 'a' 4 [`IMAGE`;`sum`];; asearcht 5 [`{x | f x } = \y. f y`];; searcht 5 [name "DLWCHEM"];; searc 'b' 4 [`3`;`face`];; searcht 15 [name "CFY"];; searcht 5 [`facet_of`;`FINITE`];; searc 'c' 0 [`lfun`;`lmfun`];; searcht 5 [`regular_spherical_polygon_area`];; searc 'd' 3 [`cos(x - y)`];; searc 'e' 0 [`cos (pi/ &6)`];; searcht 5 [`cos(acs t)`];; searcht 5 [`BIJ`;`CARD`];; searc 'f' 0 [`face_of`;`FINITE`];; searc 'g' 0 [`face_of`;`facet_of`];; BIJ_FACET2_EDGE;; BIJ_EDGES_DART_FACE;; searcht 5 [`facet_of`;`2`];; searc 'h' 4 [`dartset_leads_into_fan`;`edges`];; searc 'i' 1 [`fchanged`;`topological_component_yfan`];; searc 'j' 2 [`?`;`?!`];; searcht 25 [`fully_surrounded`;];; searcht 25 [`conforming_fan`];; searcht 5 [`facet_of`;`?`];; searc 'k' 2 [`facet_of`;`?`];; searc 'l' 1 [`polytope`;`polyhedron`];; searcht 5 [`facet_of`;`{}`];; searcht 5 [`face_of`;`SUBSET`];; searcht 5 [`p facet_of p`];; searcht 15 [name "KREIN"];; searc 'm' 0 [`polyhedron`;`convex`];; searc 'n' 0 [`polytope`;`compact`];; searc 'o' 4 [`SUBSET`;`convex hull x`];; searcht 5 [`convex hull x`;`face_of`];; searc 'p' 2 [`face_of`;`convex`];; searc 'q' 0 [`convex x`;`convex hull y = y`];; searc 'r' 0 [`extreme_point_of`;`face_of`];; searc 's' 0 [`face_of`;`facet_of`;`INTERS`];; searc 't' 0 [`CARD x = 0`];; searc 'u' 14 [`~(x = {})`];; searc 'v' 18 [`CARD x` ;`2`];; searcht 15 [`CARD`;`3`];; searcht 5 [`CARD A < CARD B`];; searc 'w' 12 [`PSUBSET`];; searc 'x' 0 [`CARD{x,y} = 2`];; searc 'y' 1 [`INTERS {}`];; searcht 15 [`(:A)`;`{x}`];; searc 'z' 0 [`aff_dim x <= aff_dim y`;`SUBSET`];; searc 'a' 0 [`aff_dim {y}`];; searcht 25 [`A = {x}`];; searc 'b' 0 [`INTERS {x}`];; searc 'd' 0 [`x ==> polyhedron p`;`face_of`];; searc 'g' 0 [`face_of`;`facet_of`];; searcht 5 [`SUBSET`;`bounded`];; searc 'h' 0 [`face_of`;`SUBSET`];; searcht 5 [`aff_dim`;`2`;`facet_of`];; searc 'k' 0 [`3`;`interior`;`aff_dim`];; searcht 5 [`ball_annulus`;`FINITE`];; searcht 5 [`x IN {}`];; searcht 5 [`CARD`;`SUBSET`];; EXISTS_M_POLYHEDRON;; searcht 5 [`CARD {}`];; searc 'l' 0 [`ball_annulus`;`norm`];; searc 'm' 0 [`arclength`;`arcV`];; searc 'n' 0 [`arclength a b c <= arclength a b c'`];; searcht 5 [`arcV a b c <= arcV a' b' c'`];; searcht 5 [`arcV a b c < arcV a' b' c'`];; searcht 5 [`arclength a b c <= arclength a' b' c'`];; searc 'p' 0 [`acs x <= acs y`];; searc 'o' 3 [`acs`;`arclength`];; searc 'q' 0 [`dist (x,y) <= dist (x,p) + dist(p,y)`];; searc 'r' 5 [`(a *a + b *b - c *c)/(&2 *a* b)`];; searc 's' 0 [`x / y <= z / y`];; searc 't' 6 [`&0 < x * y`];; searc 'u' 0 [`x * x <= y * y`];; searcht 5 [`x < acs y`];; searc 'v' 0 [`pi / &2 - acs x`];; COS_PI6;; searcht 5 [`acs (sqrt(&3)/ &2)`];; searcht 5 [`acs (x ) = pi/ &6`];; searcht 5 [`acs (cos x)`];; searc 'w' 1 [`asn (-- x)`];; searc 'x' 0 [`acs (&0)`];; searc 'y' 0 [`acs x < acs y`];; searc 'z' 0 [`acs x <= acs y`];; searcht 15 [`sqrt3`];; searcht 5 [`BIJ`;`a..b`];; searcht 5 [`BIJ`;`CARD`];; searcht 5 [`IMAGE`;`CARD`];; searcht 5 [`HAS_SIZE`;`BIJ`];; (* Nov 11, 2012 *) searcht 50 [`CARD`;`f:num->B`;`?`];; searcht 5 [def "CARD"];; searcht 5 [`ITSET`];; searcht 50 [`BIJ`];; type_of `CHOICE`;; searc 'a' 0 [`CARD A = 0`];; searc 'b' 0 [`A SUBSET {}`];; searcht 5 [`INJ`;`?`;`(f:A->B)`];; searcht 50 [`(f x = f y) ==> (x = y)`];; searc 'c' 0 [`x HAS_SIZE 0`];; searc 'u' 14 [`~(x = {})`];; searc 'e' 0 [`DELETE`;`HAS_SIZE`];; searc 'd' 1 [`DELETE`;`FINITE`];; type_of `PRE`;; searcht 5 [`A DIFF B HAS_SIZE c`];; searcht 5 [`FINITE (A DIFF B) `];; searc 'f' 1 [`CARD( A DIFF B)`];; searc 'g' 0 [`CARD (IMAGE j A)`];; searcht 5 [name "INJ_IFF_SURJ"];; searcht 5 [` (a..b) HAS_SIZE t`];; searc 'l' 0 [`ball_annulus`;`norm`];; searcht 5 [`sum V x = sum V y`];; searc 'm' 3 [`lmfun_ineq_center`];; searc 'n' 1 [`hl x`];; searc 'o' 1 [`lfun`;`lmfun`];; searcht 5 [`sum(a..n)`;`sum(b..n) f + sum (a..r) f`];; searc 'p' 1 [`sum(a..a)`];; SUM_EQ;; searcht 5 [`3 <= CARD x`;`facet_of`];; searcht 5 [`sum`;`&6 * &n - &12`];; searcht 5 [`BIJ`;`HAS_SIZE`];; searc 'q' 2 [`BIJ`;`CARD`];; searc 'r' 3 [`BIJ`;`FINITE`];; GOTCJAH;; searcht 5 [`&0 <= sol x U`];; searcht 5 [`fchanged`];; RADIAL_NORMBALL;; FCHANGED_RADIAL;; FCHANGED_MEASURABLE;; searc 's' 0 [`radial`;`radial_norm`];; SUM_EQ;; searc 't' 0 [`regular_spherical_polygon_area`];; searc 'u' 2 [`FINITE`;`facet_of`];; searc 'v' 3 [`pack_ineq_def_a`];; searc 'w' 1 [`acs_sqrt_x1_d4`];; searc 'x' 2 [`arclength_x_123`];; searc 'y' 2 [`x pow 2 <= y pow 2`];; searc 'z' 2 [`sqrt (x pow 2)`];; searc 'a' 0 [`sqrt(&4)`];; searcht 5 [`arclength x y z <= arclength x' y' z'`];; Trigonometry1.TRI_SQUARES_BOUNDS;; searc 'b' 0 [`arcV`;`arclength`];; searc 'c' 0 [`arclength a b c = arclength b a c`];; searc 'd' 0 [`ball_annulus`;`norm`];; PACK_INEQ_DEF_A_797;; searc 'e' 0 [`arcV x y z = arcV x z y`];; searcht 15 [name "plain_hyper"];; (* Nov 13, 2012 *) searcht 5 [`gamma3f_x_div_sqrtdelta`];; searcht 50 [def "gamma3f"];; searc 'a' 1 [`delta`;`ups_x`];; searcht 5 [`delta`;`delta_x`];; searc 'b' 3 [`x / y < z`];; searc 'c' 2 [`sqrt x < sqrt y`];; searc 'd' 4 [`&0 <= x/y`];; searc 'e' 5 [`&0 <= x * y`];; searc 'f' 5 [`&0 < x* y`];; searcht 5 [def "cut"];; searcht 5 [`lfun`;`h0cut`];; searcht 5 [`vol_x`;`vol_y`];; searcht 5 [`vol_y`;`sqrt`];; searc 'g' 0 [`sqrt( x * x) = x`];; searc 'h' 0 [`sqrt2 * sqrt2`];; searcht 5 [`dih_x_div_sqrtdelta_posbranch`;`dih_x`];; searcht 50 [`dih_x_div_sqrtdelta_posbranch`];; searcht 15 [name "LET"];; searc 'i' 1[`sol_y`;`sol_x`];; searc 'j' 0 [`dih_x x1 x2 x3 x4 x5 x6 = dih_x x1 x2' x3' x4' x5' x6'`];; searc 'k' 1 [`dih_x x1 x2 x3 x4 x5 x6 = dih_x x1 x2' x3' x4' x5' x6'`];; searc 'l' 1 [`sol_euler_x_div_sqrtdelta`;`delta_x`];; searc 'm' 0 [`sol_x`;`sol_euler_x`];; searc 'n' 0 [`sol_x a b c d e f = sol_x a' b' c' d' e' f'`];; searc 'o' 1 [`sol_x a b c d e f = sol_x a' b' c' d' e' f'`];; searc 'p' 0 [`dih_x_div_sqrtdelta_posbranch`;`dih_x`];; searcht 5 [`delta_x a b c d e f = delta_x a' b' c' d' e' f'`];; searc 'q' 1 [`ups_x a b c = ups_x a' b' c'`];; searc 'r' 4 [`&0 < ups_x x y z`];; searcht 5 [`sqrt(&2) * sqrt(&2)`];; searc 's' 0 [`ups_x a b c = ups_x a' b' c'`];; searcht 5 [`eulerA_x a b c d e f = eulerA_x a' b' c' d' e' f'`];; searc 't' 12 [`&0 < x * y`];; searcht 5 [`sqrt x <= sqrt y`];; searcht 5 [`eta_y`;`&2 * x`];; searcht 5 [`x * x <= y * y`];; searcht 5 [`sqrt8 * sqrt8`];; searc 'u' 13 [`dih_x_div_sqrtdelta_posbranch`];; searc 'w' 0 [`dih_x`;`atn2`];; searc 'v' 5 [`atn2`;`pi`;`<=`];; searc 'w' 5 [`atn`;`<`;`pi`];; searcht 50 [`&0 <= a * b`];; searcht 10 [`dih4_x_div_sqrtdelta_posbranch`];; searcht 5 [`eta_y`;`&0 < delta_x`];; searcht 5 [`&0 <= ups_x a b c`];; cell_3_delta_x_pos_x;; (* &0 < delta_x <=> (eta_x < sqrt2 *) UPS_X_POS;; delta_x4_pos;; searcht 10 [`delta_x`;`ups_x`];; GSYM delta_delta_x;; Collect_geom.DELTA_RRR_INTERPRETE;; searcht 5 [`sqrt8 * sqrt8`];; searc 'x' 0 [`&0 <= x pow 2`];; searc 'y' 0 [`eta_y a b c = eta_y a' b' c'`];; searc 'z' 0 [`sqrt8`;`sqrt2`];; searcht 5 [`delta_x a b c d e f = delta_x a' b' c' d' e' f'`];; searc 'a' 0 [`sqrt8 * sqrt8`];; searcht 5 [`radV`];; (* Nov 18, 2012 *) searcht 5 [`gamma3f_x_div_sqrtdelta`];; searcht 5 [`sol_euler_x_div_sqrtdelta a b c d e f = sol_euler_x_div_sqrtdelta a' b' c' d' e' f'`];; searc 'b' 0 [`eta_x a b c = eta_x a' b' c'`];; searcht 5 [`gamma3f a b c r s = gamma3f a' b' c' r' s'`];; searc 'h' 0 [`sqrt2 * sqrt2`];; searc 'i' 0 [`sol_x a b c d e f = sol_x a' b' c' d' e' f'`];; searc 'j' 1 [`sol_x a b c d e f = sol_x a' b' c' d' e' f'`];; searc 'k' 1[`sol_y`;`sol_x`];; searc 'l' 0 [`dih_y a b c d e f = dih_y a' b' c' d' e' f'`];; searc 'm' 1 [`dih_y a b c d e f = dih_y a' b' c' d' e' f'`];; searc 'n' 23 [`!y. (p ==> q y)`; `p ==> (!y. q y)`];; searcht 5 [`&0 <= eta_x a b c`];; searcht 6 [`&0 <= x*y`];; searcht 5 [`&0 <= x*x`];; searcht 5 [`&0 <= y_of_x dih4_x_div_sqrtdelta_posbranch a b c d e f`];; searc 'o' 0 [`hminus`;`h0`];; searc 'p' 0 [`h0cut y = &1`];; searc 'q' 0 [`hplus`;`h0`];; searc 'r' 0 [`h0cut y = &0`];; type_of `h0cut`;; bb 30;; bb 5;; bb 12;; searc 's' 0 [`gamma3f a b c d e = gamma3f a' b' c' d' e'`];; searc 't' 0 [`eta_y a b c = eta_y a' b' c'`];; searcht 5 [`ineq u T`];; (* Nov 22, 2012 *) searcht 15 [`x * y < x' * y' `];; searc 'a' 1 [`gamma2_x1_div_a`;`gamma2_x_div_azim`];; searc 'b' 0 [`h0cut y = &0`];; searc 'c' 0 [`h0`;`hplus`];; searcht 5 [`h0cut`;`lfun`];; searcht 500 [`rad2_y`];; searcht 5 [name "RHUFIIB"];; searcht 5 [`rho_ij`;`rho_x`];; searc 'd' 11 [`x <= y/ z`];; searcht 5 [`sqrt x pow 2 `];; searcht 5 [`x/ y * z`];; searcht 5 [`x /y <= z`];; searc 'e' 1 [`ups_x a b c = ups_x a' b' c'`];; searc 'f' 1 [name "RHUFIIB"];; searc 'g' 0 [`delta`;`delta_x`];; searcht 5 [`&0 <= x pow 2`];; searc 'h' 0 [`sqrt8`;`sqrt2`];; searcht 5 [`hminus`;`DECIMAL`];; searcht 1 [`rad2_x`;`rad2_y`];; searcht 5 [`eta_y a b c < sqrt2`];; searcht 15 [`x < sqrt y`];; searcht 5 [`hplus`;`DECIMAL`];; searc 'i' 0 [`rad2_x x1 x2 x3 x4 x5 x6 = rad2_x a b c d e f`];; searcht 5 [`delta_x a b c d e f = delta_x a' b' c' d' e' f'`];; searcht 5 [def "wt"];; searcht 5 [`wtcount6_y`];; bb 4;; searc 'j' 0 [`beta_bump_y`;`beta_bump_lb`;omit `ineq`];; searcht 5 [`x / y <= x / z`];; bb 3;; searcht 5 [`beta_bump_y`;`beta_bump_lb`;omit `ineq`];; searcht 5 [`if a then b else c = b`];; searcht 5 [`norm2hh`;`gamma4fgcy`];; searcht 5 [`gamma23_full8_x`];; searcht 5 [`gamma3_x`;];; searcht 5 [`vol3f_456`];; searcht 5 [`critical_edge_y`];; searc 'k' 0 [`sqrt2 * sqrt2`];; searc 'l' 1 [`sol_y`;`sol_x`];; searcht 5 [`sqrt (y * y)`];; searc 'm' 0 [`lfun`;`h0cut`];; searc 'n' 1 [`lmfun x = lfun x`];; searc 'o' 0 [`hminus`;`h0`;omit `ineq`];; searcht 5 [`dih_x a b c d e f = dih_x a' b' c' d' e' f'`];; searcht 5 [`x * y <= x * z`];; searcht 5 [`#0.008`;`gamma2_x_div_azim`];; searcht 5 [`gamma2_x1_div_a`;`gamma2_x_div_azim`];; searcht 5 [`atn2 (x,y) + atn2 (u,v)`];; searc 'q' 3 [`tan (x + y)`];; searc 'p' 2 [`tan x = tan y`];; searcht 5 [`tan (atn x)`];; searcht 5 [`abs(atn x) < pi / &2`];; searcht 15 [`cos x = &0`];; searc 'r' 7 [`atn2(x,y)`];; searcht 5 [`&0 < atn x`];; searc 's' 7 [ `atn2`;`atn`];; searcht 5 [`atn x < atn y`];; searcht 35 [`y < u / x`];; searcht 5 [`delta_x`;`ups_x`];; Sphere.dih_x;; searc 't' 0 [`sqrt (x pow 2)`];; fynlist 3;; follow_your_nose_string_list();; searcht 5 [`sqrt x * sqrt y`];; searcht 5 [`sqrt (x1 pow 2)`];; searc 'u' 1 [`atn2 (a* x,a*y)`];; ETA_Y_BOUNDS;; searc 'v' 4 [`gamma3f_x_div_sqrtdelta`;`gamma3f`];; searcht 50 [`dih4_x_div_sqrtdelta_posbranch`;omit `ineq`];; dih_x_div_sqrtdelta_pos;; searc 'w' 1 [`&0 < delta_x4 a b c d e f`];; searcht 5 [`sqrt8 * sqrt8`];; searcht 5 [`x * x < y * y`];; searc 'x' 1 [`h0cut y = &1`];; searcht 5 [`x * y < x * z`];; searcht 5 [`dih4_x_div_sqrtdelta_posbranch`;`dih_x_div_sqrtdelta_posbranch`];; bb 22;; bb 3;; searcht 5 [`dih_y a b c d e f = dih_y a' b' c' d' e'f 'f`];; searcht 5 [`eta_y a b c = eta_y a' b' c'`];; searcht 5 [`gamma3f a b c d e = gamma3f a' b' c' d' e' `];; searcht 15 [`x <= y/z`];; searcht 35 [`dih_y_div_sqrtdelta_posbranch a b c d e f = dih_y_div_sqrtdelta_posbranch a' b' c' d' e' f'`];; searcht 5 [`dih_x_div_sqrtdelta_posbranch`;`dih_x`];; searc 'y' 0 [`(?x. p /\ q x) <=> (p /\ ?x. q x)`];; searcht 5 [`gamma2_x1_div_a`;`gamma2_x_div_azim`];; searcht 5 [name "VICUATE"];; searcht 5 [def "wedge"];; (* Nov 29, 2012 *) bb 3;; searcht 5 [`gamma4fgcy a b c d e f l = u a' b' c' d' e' f' l`];; searcht 5 [`rad2_y`;`eta_y`;omit `ineq`];; searc 'a' 0 [`sqrt8`;`sqrt2`];; Sphere.delta_y;; Sphere.bump;; searcht 5 [`m1`;`pi`];; searcht 5 [`wedge a b c d INTER wedge a' b' c' d'`];; searcht 5 [name "WEDGE_ORDER_DIS"];; searcht 5 [`wedge_ge a b c d INTER wedge_ge a' b' c' d'`];; searcht 5 [`wedge`;`wedge_ge`];; searcht 25 [`&2 * pi`;`azim`];; searcht 15 [`azim a b c d = &0`];; Local_lemmas.AZIM_EQ_0_GE_ALT2;; searcht 5 [`x IN Y <=> x IN Z`];; searcht 5 [`wedge_ge`;`azim`];; searcht 5 [`&0 <= azim a b c d `];; searcht 15 [`collinear`;`aff_ge`];; searc 'b' 3 [`azim a b c d + azim a b d e`];; searcht 5 [`collinear {a,b,c} ==> (c IN affine hull X)`];; searcht 5 [`aff_ge X {}`];; searcht 25 [`collinear {a,b,c}`];; searc 'c' 4 [`aff_ge`;`aff`];; searc 'd' 2 [`aff_ge X Y SUBSET aff_ge X' Y'`];; searcht 35 [`x IN aff_ge X Y`;omit `azim`;omit `%`];; searc 'e' 22 [`affsign`];; searcht 35 [`affsign`];; searcht 5 [`DISJOINT`;`aff_ge S U`];; searcht 5 [`x IN aff_ge {x} U`];; AFF_GE_MONO_RIGHT;; SUBSET;; searcht 5 [`x IN X /\ X SUBSET Y`];; searcht 5 [`aff_ge S {}`];; searcht 5 [`x IN u hull v`];; searcht 5 [`collinear`;`~(x = y)`];; searcht 15 [`wedge`;`wedge_ge`];; searcht 15 [`&0 <= azim a b c d `];; searcht 15 [`wedge`;`azim`];; searcht 15 [`collinear`;`affine hull X`];; AFFINE_HULL_3_IMP_COLLINEAR;; searcht 15 [`affine hull X`;`aff_ge`];; searcht 5 [`X INTER {u}`];; searcht 15 [`X INTER Y = {}`;`!`];; searcht 5 [`azim`;`aff_ge X Y`];; searcht 15 [`azim a b c d = azim a b c d'`;omit `norm`];; searcht 15 [`azim a b c d = &0`];; searcht 15 [`aff_gt`;`aff_ge`];; searcht 5 [`azim a b c c`];; (* Dec 1, 2012 *) searcht 5 [`&x < &y`];; bb 6;; searcht 50 [`beta_bump_y`];; Sphere.beta_bump_y;; searcht 5 [`x /y`;`inv`];; searcht 5 [`inv x <= inv y`];; searcht 5 [`hminus`;`hplus`];; searcht 5 [`hplus`;`sqrt8`];; searc 'a' 0 [`sqrt8`;`sqrt2`];; searcht 5 [`dih_y a b c d e f = dih_y a' b' c' d' e'f 'f`];; searcht 3 [`rad2_y`;`y_of_x`];; searc 'b' 1 [`norm2hh`;omit `ineq`];; (* Dec 5, 2012 *) searcht 5 [`sum`;`IMAGE`];; Counting_spheres.BIJ_SUM;; searcht 55 [`x MOD n`;`(v = q * x + (b:num))`];; searcht 5 [`MOD`;`DIV`];; DIVISION;; searcht 5 [`x IN a..b`;`?`;`x+(a:num)`];; searcht 5 [`(a - b) MOD n`];; searcht 30 [`MOD`];; searcht 5 [`a <= (b:num)`;`a >= (b:num)`];; searcht 30 [`DIV`];; MOD_EQ_0;; searcht 30 [`(x - y) * (n:num) = x * n - y * n`];; searc 'c' 0 [`(x * y + a ) MOD n`];; searcht 5 [`a MOD n = a`];; searcht 5 [`sum {}`];; searcht 5 [`CARD X = 0`];; searcht 5 [`~(X = {})`;`?`];; searcht 5 [name "STRONG";name "INDUCT"];; searcht 5 [`{} INTER X`];; bb 8;; (* Dec 14, 2012 *) searcht 5 [`CARD x = 0`];; searcht 15 [`(X = {})`;`?`];; searcht 5 [`~(!x. P x)`];; searcht 15 [`&0 <= sum X f`];; searcht 15 [`sum {i}`];; searcht 15 [`i..i`];; searcht 5 [`x IN Y <=> x IN Z`];; searcht 15 [`EL 0 x`];; searcht 5 [`HAS_SIZE`;`0`;`{}`];; bb 9;; searcht 5 [`x HAS_SIZE (SUC n)`];; searcht 5 [`( k * n + i) MOD n`];; Print_types.print_goal_types();; searcht 5 [`i MOD n = i`];; searcht 5 [`0 MOD n`];; searcht 5 [`periodic`;`cc_qu_v9`;omit `a_spine5`];; searcht 50 [`sum (a..b) f`;`f a + sum (c..d) f`];; searcht 5 [`sum (a..b) f`;`(b:num) < a`];; searcht 5 [`sum (n..n) f`];; searcht 5 [`sum X f = sum X g`];; (* Dec 21, 2012 *) searcht 5 [name "MHFTT"];; searcht 5 [`collinear`;`aff_dim`];; searcht 5 [name "IDBEZ"];; searcht 5 [`voronoi_list`;`omega_list`];; searcht 15 [`barV`;`aff_dim`];; searcht 5 [`aff_dim`;`segment`];; searcht 5 [`segment`;`face_of`];; searcht 5 [`segment`;`extreme_point_of`];; searc 'a' 0 [`extreme_point_of`;`face_of`];; FACE_OF_REFL;; searcht 5 [`polytope`;`voronoi_list`];; searcht 5 [`segment`;`hull`];; searcht 5 [`{x} face_of p`];; searcht 5 [`aff_dim`;`facet_of`];; searcht 5 [`segment`;`aff_dim`];; searc 'b' 8 [`segment`;`~(a = b)`];; searc 'c' 0 [`aff_dim {c}`];; searcht 5 [`aff_dim x = &0`];; searcht 5 [name "YNHY"];; searcht 5 [name "BARV_3_EXPLICIT"];; searcht 5 [name "TRUNCATE_SIMPLEX_EXPLICIT_3"];; searcht 5 [name "LEFT_ACTION_LIST_PROPERTIES"];; searcht 5 [name "OMEGA_LIST_2_EXPLICIT_NEW"];; searc 'd' 0 [`permutes`;`hl`;`barV`];; searcht 5 [`p permutes a..b ==> p permutes c..d`];; searcht 50 [`u ==> x permutes y`];; searcht 15 [`truncate_simplex 2 (CONS x y)`];; searcht 15 [`set_of_list (CONS x y)`];; searcht 15 [`hl x `;` (left_action_list p q)`];; searcht 15 [`hl`];; searcht 15 [`barV V k (truncate_simplex a b)`];; searcht 15 [`left_action_list`;`swap`];; searcht 15 [`TABLE`];; searcht 15 [`EL i x = EL i y`];; searcht 15 [`LENGTH`;`TABLE`];; searcht 15 [`inverse (swap(a,b))`];; searcht 5 [`EL j (truncate_simplex k p)`];; EL;; (* Dec 22, 2012 *) searcht 15 [def "circ"];; searcht 15 [name "MHFT"];; searcht 15 [`affine hull (convex hull s)`];; searc 'e' 14 [`affine hull {a,b}`];; searcht 15 [`voronoi_list`;`dist`];; searcht 5 [`norm x pow 2`;`dot`];; searcht 15 [`voronoi_closed`;`voronoi_list`];; Packing3.VORONOI_LIST_SUBSET_VORONOI_CLOSED;; searcht 15 [def "voronoi_closed"];; searcht 15 [`omega_list`;`voronoi_list`];; searcht 5 [name "XYOF"];; searcht 5 [`barV`;`x SUBSET V`];; bb 4;; searcht 5 [`affine_dependent`;`barV`];; searcht 5 [`dist(x,y) < dist (u,v)`];; searcht 5 [`EL x y IN set_of_list p`];; searc 'f' 0 [`x IN set_of_list p`];; searc 'h' 1 [`MEM x u`;`EL`];; searcht 5 [`aff_dim`;`barV`];; searcht 15 [`truncate_simplex`;`set_of_list`];; searc 'g' 0 [`EL`;`truncate_simplex`];; searc 'h' 0 [`LENGTH (truncate_simplex a b)`];; searcht 5 [`aff_dim X <= aff_dim Y`];; searcht 5 [`barV`;`aff_dim`];; searcht 5 [`voronoi_closed`;`bis`];; searcht 5 [`voronoi_closed`;`dist`];; searcht 5 [`x IN s ==> x IN convex hull s`];; searcht 15 [`barV`;`circumcenter`];; searcht 10 [`omega_list`;`voronoi_list`;`barV`];; searcht 10 [`circumcenter`;`dist`];; searcht 5 [`sqrt x = sqrt y`];; searcht 5 [`HD (truncate_simplex k u)`];; searcht 15 [`&0 < x * y`;`&0 < x`];; (* Dec 23, 2012 *) searcht 15 [`CONS`;`LENGTH`;`3`];; searcht 15 [`CONS`;`(x:(A)list) = y`];; searcht 15 [`LENGTH t = 0`];; searcht 15 [`set_of_list (CONS x y)`];; searc 'i' 15 [`affine hull {a,b,c}`];; searcht 8 [`(a cross b) dot c`];; searcht 5 [`a cross a`];; searcht 5 [`(vec 0) dot b`];; searcht 5 [`coplanar`;`cross`];; searcht 5 [`aff_dim`;`coplanar`];; searcht 15 [`aff_dim`;`INSERT`];; searcht 5 [`coplanar`;`affine_dependent`];; searcht 50 [`coplanar`];; searcht 5 [`aff_dim x <= aff_dim y`];; searcht 5 [`aff_dim`;`{a,b,c}`];; searcht 5 [`aff_dim (affine hull s)`];; searcht 5 [`aff_dim {a,b}`];; searcht 5 [`barV`;`aff_dim`];; searcht 5 [`x IN y <=> x IN z`];; searcht 5 [`affine hull (convex hull s)`];; searcht 5 [`y SUBSET affine hull y`];; searcht 5 [`t % x = t % y`];; searcht 5 [`circumcenter x IN affine hull y`];; searcht 15 [`&0 < a * b`];; searc 'j' 1 [`extreme_point_of`;`segment`];; searcht 5 [`aff_dim {a}`];; searcht 5 [`aff_dim`;` {a,b}`];; searcht 5 [`aff_dim`;`convex hull x`];; searcht 5 [`face_of`;`extreme_point_of`];; searcht 5 [`segment`;`convex`];; searcht 15 [`X SUBSET aff_gt U V`];; searcht 5 [`aff_gt {x,y} {z}`];; searcht 5 [`set_of_list ul`;`LENGTH`];; searcht 5 [`collinear {a,b}`];; searcht 5 [`truncate_simplex i ul = ul`];; searcht 5 [`x IN S ==> x IN (convex hull S)`];; searcht 5 [`set_of_list (truncate_simplex i ul)`];; searcht 5 [`EL i ul IN set_of_list ul`];; searcht 5 [`MEM (EL i ul) ul`];; searcht 5 [`EL k (truncate_simplex i ul)`];; searcht 5 [`convex hull X SUBSET aff_ge X Y`];; searcht 4 [`aff_ge X Y = aff_ge X Z`];; searcht 5 [`convex hull X`;`aff_ge`];; searcht 5 [`aff_ge X Y SUBSET aff_ge X' Y'`];; searcht 25 [`aff_ge {a,b,c} {d}`];; searc 'k' 1 [`coplanar`;`DISJOINT`];; searcht 5 [`coplanar`;`aff_dim`];; searcht 15 [`aff_dim (r:real^A->bool) <= x`];; searcht 5 [`dimindex (:3)`];; searcht 5 [`x IN interior (UNIV)`];; searcht 5 [`aff_dim`;`(UNIV)`;`affine hull x`];; searcht 5 [`affine hull {a,b,c,d}`];; searcht 5 [name "JBD"];; searcht 5 [`a cross (b+ c)`];; searcht 5 [`(a + b) dot c`];; searcht 5 [`vec 0 dot a`];; searcht 5 [`-- (x dot y)`];; searcht 5 [`-- (x cross y)`];; searcht 15 [def "wedge"];; searcht 15 [`wedge`;`open`];; searcht 5 [`convex`;`&1`;`%`];; searcht 5 [`convex hull S = S`];; searcht 3 [`(a + b) cross d`];; searcht 5 [`convex hull A SUBSET convex hull b`];; searcht 5 [`convex`;`omega_list`];; searcht 5 [`convex hull {a,b,c,d}`;`%`];; searcht 5 [`vec 0 dot u`];; searcht 5 [`re_eqvl a (t * b)`];; searc 'l' 2 [`re_eqvl`];; searcht 5 [`&0 < inv x`];; searcht 5 [`barV`;`aff_dim`];; searcht 5 [`INSERT`;`aff_dim`];; searcht 5 [`convex hull x`;`mxi`];; searcht 50 [`mxi`];; between;; searcht 5 [`between`;`a % b`]; searcht 5 [`between`;`segment`];; searcht 5 [`segment`;`a % b`];; searcht 5 [`omega_list_n`;`omega_list`];; searcht 5 [`omega_list`;`circumcenter`];; searcht 5 [`truncate_simplex k ul = ul`];; searcht 5 [` &0 % x`];; searcht 5 [`x + vec 0`];; searcht 5 [`hl`;`dist`];; searcht 5 [`HD`;`EL 0`];; searcht 5 [`a % u + b % v IN f hull s`];; searcht 5 [`a + b IN affine hull s`];; searcht 25 [`a % u`;`affine`];; searcht 5 [`affine (affine hull s)`];; searcht 5 [`circumcenter x IN affine hull s`];; searcht 5 [`cc_cell`;`convex`];; searcht 15 [`convex hull y SUBSET x`;`convex u`];; searcht 5 [`S SUBSET affine hull S`];; searcht 5 [`convex hull s = s`];; searcht 5 [`mcell2`;`voronoi_closed`];; searcht 5 [`vol`;`convex hull {a,b,c,d}`];; searcht 5 [`coplanar`;`delta`];; searcht 15 [`coplanar`;`vol`];; searcht 5 [name "POLFLZY"];; searcht 5 [`delta_x`;`delta`];; searcht 5 [`coplanar`;`coplanar_alt`];; searcht 5 [`dimindex (:3)`];; searcht 5 [`&0 <= delta a b c d e f`];; Rogers.MHFTTZN1;; searcht 5 [`mcell4`;`convex hull s`];; searcht 5 [`mcell4`;`coplanar`];; searcht 5 [`coplanar`;`aff_dim`];; searcht 5 [`aff_dim x <= aff_dim y`];; searcht 5 [`s SUBSET f hull s`];; searcht 5 [`convex`;`mcell`];; searc 'a' 0 [`convex hull s SUBSET affine hull s`];; searc 'b' 0 [`x IN s /\ s SUBSET t`];; searcht 5 [`set_of_list (truncate_simplex k vl)`];; searcht 5 [`s SUBSET affine hull s`];; searcht 5 [`affine hull s SUBSET affine hull t`];; searcht 5 [`affine hull (affine hull s)`];; searcht 5 [`coplanar {a,b,c}`];; searcht 5 [`LENGTH(truncate_simplex k vl)`];; searcht 25 [`circumcenter`];; searcht 5 [`affine_dependent`;`collinear`];; searcht 5 [`truncate_simplex k vl`;` barV V k`];; AFFINE_DEPENDENT_IMP_COLLINEAR_3;; searcht 5 [`EL k (truncate_simplex j ul)`];; searcht 5 [`mxi`;`dist`];; searc 'c' 3 [`omega_list_n`;`voronoi_list`];; searcht 5 [`convex`;`voronoi_list`];; searcht 5 [`between`;`mxi`];; searcht 5 [`between`;`convex hull s`];; searc 'd' 0 [`convex hull a SUBSET convex hull b`];; searcht 5 [`convex hull s = s`];; searcht 5 [`voronoi_set`;`dist`];; searcht 15 [`(?v. p v) ==> t`];; searcht 15 [`~(x = {})`;`?`];; searcht 15 [`set_of_list ul SUBSET V`];; searcht 15 [`q IN set_of_list (truncate_simplex k vl)`];; bb 5;; searcht 5 [`radV`;`dist`];; searcht 5 [`collinear`;`leaf`];; searcht 5 [`coplanar`;`SUBSET`];; searcht 5 [`s SUBSET f hull s`];; searcht 5 [`aff_dim`;`coplanar`];; searcht 5 [`aff_dim`;`collinear`];; searcht 5 [`x UNION {y} = y INSERT x`];; type_of `INSERT`;; searcht 5 [`aff_dim`;`INSERT`];; type_of `mcell`;; searcht 5 [def "rog"];; searcht 5 [`rogers`;`omega_list_n`];; searcht 5 [`rogers`;`aff_ge`];; searcht 5 [`aff_ge`;`convex`];; searcht 15 [`aff_ge a b = aff_ge c d`];; searcht 15 [`mcell2`;`aff_ge`];; searcht 5 [`aff_gt`;`aff_ge`];; searcht 15 [`aff_gt {a,b}`];; searcht 5 [`aff_ge a b SUBSET aff_ge c d`];; searcht 15 [`FINITE`;`aff_dim`];; searcht 5 [`?(x:real^A). p`;`~(x = (a:real^A))`];; searcht 5 [`DISJOINT`;`collinear`];; searcht 5 [`{} SUBSET X`];; searcht 5 [`aff_ge S {}`];; searcht 5 [`affine`;`aff`];; searcht 5 [def "aff"];; searcht 15 [def "aff"];; searcht 35[`affine_dependent`];; searcht 5 [`affine hull s`;`aff_ge`];; searcht 5 [`collinear`;`affine hull {a,b}`];; searcht 5 [`collinear`;`aff_dim`];; searcht 5 [`aff_dim {a,b}`];; searcht 5 [`aff_dim {a,b,c} = &2`];; searcht 5 [`affine hull s = affine hull t`;`aff_dim`];; searcht 5 [`x IN s ==> x IN f hull s`];; searcht 5 [`coplanar`;`aff_dim`];; searcht 5 [`aff_dim (affine hull s)`];; searcht 5 [`affine hull (affine hull x)`];; searcht 5 [`affine hull {a,b,c}`;`%`];; searcht 5 [`%`;`conv`];; searcht 5 [`affine hull {a,b}`;`%`];; searcht 5 [`%`;`aff_ge {a,b} {c,d}`];; searcht 5 [`conv`;`convex hull s`];; searcht 5 [def "conv"];; searcht 5 [`aff_ge`;`conv`];; searcht 50 [`conv`];; bb 5;; searcht 5 [`a % v = a % w`];; searcht 5 [`a % (b + c)`];; searcht 5 [`a % b % c`];; searcht 5 [`collinear`;`DISJOINT`];; searcht 5 [`affine_dependent`;`~`;`{a,b,c,d}`];; AFFINE_DEPENDENT_EXPLICIT;; searcht 8 [`vsum`;`INSERT`];; searcht 5 [`CARD`;`DISJOINT`];; searcht 5 [name "CARD4_IMP_DISTINCT"];; VSUM_CLAUSES;; CONJUNCT1 VSUM_CLAUSES;; (* Dec 27, 2012 *) searc 'a' 0 [`coplanar {a,b,c}`];; searcht 5 [`s SUBSET f hull s`];; searc 'b' 1 [`DISJOINT`;`coplanar`];; searcht 5 [`%`;`aff_gt {a,b} {p}`];; searcht 5 [`%`;`aff_ge {a,b} {p}`];; searcht 5 [`DISJOINT`;`collinear`];; searcht 5 [`%`;`affine hull {a,b,p}`];; searcht 5 [`affine_dependent`;`coplanar`];; searcht 5 [`coplanar`;`CARD`];; searcht 5 [`CARD {a,b,c,d}`];; searcht 5 [`coplanar`;`coplanar_alt`];; searcht 5 [`dimindex (:3)`];; searcht 15 [`affine_dependent {a,b,c,d}`];; searcht 5 [`aff_dim`;`coplanar`];; searc 'c' 0 [`(&0 <= w * t3) <=> p`];; searcht 5 [`affine hull {a,b}`;`%`];; searcht 15 [`mxi`];; searcht 15 [`convex hull {a,b,c}`];; searcht 5 [`&0 <= inv x `];; searcht 5 [`abs(a * b)`];; searcht 5 [`%`;`aff_gt {a,b,c} {p}`];; searcht 5 [`DISJOINT`;`coplanar`];; searcht 5 [`x INTER x`];; searcht 5 [`convex hull {a,b,c,d}`;`%`];; searcht 5 [`a/b < c`];; searcht 15 [`coplanar {a,b,c,d}`];; searcht 5 [`chi_msb [a;b;c]`;`%`];; searcht 5 [`aff_gt`;`affine hull s`];; searcht 5 [`x = [a;b;c]`;`3`];; searcht 5 [`coplanar {a,b,c}`];; searcht 5 [`coplanar (affine hull s)`];; searcht 5 [`coplanar`;`SUBSET`];; searcht 5 [`convex`;`mcell_set`];; searc 'd' 1 [`convex`;`rcone_ge`];; searcht 5 [`&0 <= hl ul`];; searcht 5 [`convex`;`aff_ge`];; searc 'e' 0 [`hl [a;b]`];; searcht 5 [`truncate_simplex 1`];; searcht 5 [`convex {}`];; searc 'f' 0 [`convex (convex hull s)`];; searcht 50 [`edgeX`];; searcht 50 [`VX`];; searcht 5 [`rogers`;`voronoi_closed`];; searcht 5 [`rogers`;`VX`];; searcht 5 [`VX`;`mcell`];; searcht 15 [`voronoi_closed V v INTER x`];; searcht 15 [`voronoi_set V {u,v}`];; searcht 5 [`dist(x,w) = &0`];; searcht 5 [`&0 <= dist (x,y)`];; Hdtfnfz.HDTFNFZ;; searcht 5 [`cell_params`];; searcht 5 [`(\(a,b). f a b) t`];; searcht 5 [`NULLSET`;`vol`];; searcht 15 [`cell_params`];; searcht 15 [`barV`;`HD vl IN V`];; searcht 5 [`barV`;`set_of_list ul SUBSET V`];; searcht 5 [`sqrt(&4)`];; searcht 50 [`NULLSET`];; COPLANAR_IMP_NEGLIGIBLE;; CHI_MSB_COPLANAR;; searcht 5 [`aff_dim`;`barV`];; searcht 5 [`convex hull X SUBSET convex hull Y`];; searcht 15 [`edgeX`];; searcht 5 [`convex hull X = X`];; CC_CELL34;; ZASUVOR;; searcht 5 [`x SUBSET f hull y`];; searcht 5 [`p IN aff_gt s {p}`];; searcht 5 [`chi_msb`;`coplanar`];; searcht 10 [`coplanar {a,b,c,d}`;`%`];; searcht 15 [`affine_dependent`;`{a,b,c,(d:real^3)}`];; searcht 5 [`affine_dependent`;`aff_dim`];; searcht 5 [`aff_dim x <= aff_dim y`;`x = y`];; searcht 5 [`aff_dim (:real^A)`];; searcht 5 [`aff_dim`;`coplanar`];; searcht 5 [`affine hull {a,b,c,d}`];; searcht 15 [`(&0 < z) ==> u`;`&0 < x * y`];; searcht 5 [`aff_gt {a,b,c} {d}`;`%`];; searcht 5 [`collinear`;`DISJOINT`];; searcht 5 [`x IN convex hull (x INSERT y)`];; (* Dec 29, 2012 *) searcht 5 [`%`;`aff_gt {a,b} {c}`];; searcht 5 [name "chi_msb_add"];; Fan.th3a;; GBEWYFX;; searcht 5 [`coplanar`;`chi_msb`];; bb 15;; searcht 5 [name "AJRI"];; searcht 5 [`coplanar`;`NULLSET`];; searcht 5 [`convex hull x SUBSET convex hull y`];; HULL_INC;; searcht 15 [`a hull X = X`];; searcht 5 [`convex`;`mcell`];; searcht 5 [`barV`;`cc_uh`];; searcht 5 [`convex hull s SUBSET convex hull y`];; searcht 5 [`f hull (f hull s)`];; HULL_INC;; searcht 5 [`NULLSET`;`SUBSET`];; searcht 5 [`NULLSET`;`vol`];; searcht 5 [`SUBSET`;`measure`];; searcht 25 [ `negligible`;`SUBSET`];; searcht 5 [`X INTER Y = Y INTER X`];; cc_cell;; bb 4;; searcht 5 [`NULLSET`;`coplanar`];; searcht 5 [`coplanar`;`vol`];; searcht 5 [name "ZWV"];; searcht 5 [name "RVF"];; Pack_defs.mcell_set;; searcht 5 [`mcell_set`;`cc_cell`];; searcht 30 [`VX`];; searcht 15 [`convex hull j`;`rogers`];; searcht 15 [`rogers`;`voronoi_closed`];; searcht 15 [`EL`;`left_action_list`];; Packing3.EL_LEFT_ACTION_LIST;; searcht 15 [`set_of_list`;`left_action_list`];; Packing3.SET_OF_LIST_LEFT_ACTION_LIST;; searcht 5 [`set_of_list [a;b;c;d]`];; set_of_list4;; searcht 5 [`CARD {a,b,c,d}`];; searcht 5 [name "WQP"];; searcht 5 [name "AJR"];; searcht 15 [`convex hull s = convex hull t`];; EXTREME_POINTS_OF_CONVEX_HULL_EQ;; Packing3.CONVEX_HULL_EQ_EQ_SET_EQ;; Rogers.WQPRRD4;; searcht 5 [`coplanar (convex hull s)`];; searcht 5 [`coplanar`;`convex hull s`];; searcht 5 [`coplanar`;`affine hull s`];; searcht 5 [`coplanar s`;`s SUBSET t`];; searcht 5 [`convex hull s SUBSET affine hull s`];; MCELL3_NONPLANAR;; searcht 5 [`truncate_simplex 2 (cc_uh V ul)`];; cc_uh;; searcht 5 [`X INTER X`];; (* Dec 30, 2012 *) CC_CELL34;; searcht 5 [`affine_dependent`;`coplanar`];; searcht 5 [`affine_dependent`;`aff_dim`];; searcht 5 [`CARD`;`coplanar`];; searcht 5 [`CARD {a,b,c,d}`];; searcht 5 [`coplanar`;`coplanar_alt`];; searcht 5 [`coplanar`;`affine hull s`];; searcht 5 [`coplanar`;`SUBSET`];; ZWVCBMN;; searcht 5 [`FINITE`;`INSERT`];; searcht 5 [`aff_dim {a,b,c,d}`];; searcht 5 [`coplanar`;`aff_dim`];; searcht 5 [`aff_dim`;`dimindex`];; searcht 5 [`cc_uh`;`barV`];; searcht 5 [`set_of_length`;`INSERT`];; EL_CC_UH;; K4_CHI_MSB_POS;; set_of_list2;; searcht 5 [`set_of_list`;`truncate_simplex 1`];; searcht 5 [`EL`;`truncate_simplex`];; searcht 20 [`LENGTH`;`truncate_simplex`];; LENGTH3;; LENGTH4_SET2;; searcht 5 [`CARD`;`4`;`cc_uh`];; set_of_list4_explicit;; LIST_OF_CC_UH;; searcht 5 [`truncate_simplex 2 (cc_uh V ul)`];; searcht 5[`sqrt(&4)`];; searcht 5 [`set_of_list`;`barV`];; searcht 5 [`HD ul`;`packing V`];; Packing3.BARV_SUBSET;; Packing3.BARV_IMP_HD_IN_SET_OF_LIST;; searcht 5 [`x IN Y /\ Y SUBSET Z`];; searcht 5 [`barV`;`set_of_list ul SUBSET V`];; searcht 5 [`A SUBSET B /\ B SUBSET A`];; searcht 15 [`cc_ke V ul = 4`];; searcht 5 [name "CARD4"];; searcht 5 [`CARD {EL 0 ul,b,c,d}`];; searcht 5 [`{a,b} = {c,d}`];; bb 6;; searcht 5 [`{a,b,c} = {a',b',c'}`];; searcht 5 [`(A =B) <=> (B = A)`];; searcht 5 [``;`barV`];; searcht 50 [`left_action_list`];; searcht 5 [`CARD`;`DIFF`];; (* Dec 31, 2012 *) Pack_defs.HL;; searcht 5 [name "RDW"];; Rvfxzbu.RVFXZBU;; searcht 5 [`TSKAJXY_statement`];; Marchal_cells_3.LEFT_ACTION_LIST_3_EXISTS;; Marchal_cells_3.LEFT_ACTION_LIST_2_EXISTS;; Rvfxzbu.RVFXZBU;; searcht 5 [`left_action_list`;`mcell`];; CARD_DIFF;; searcht 5 [`left_action_list`;`barV`];; Rogers.YIFVQDV_1;; searcht 5 [`cell_cluster_estimate`];; searcht 50 [`left_action_list`;`mcell`];; Marchal_cells_2_new.LEFT_ACTION_LIST_PROPERTIES;; searcht 5 [`convex hull s`;`mcell3`];; searcht 5 [name "REUH"];; searcht 5 [`{a,b} = {c,d}`];; searcht 5 [`VX`];; searcht 5 [`VX`;`set_of_list`];; searcht 5 [`cell_params`];; searcht 15 [`mcell4 V ul = mcell4 V vl`];; searcht 25 [` x IN mcell i V vl`];; searcht 5 [`x IN mcell2 V vl`];; Urrphbz1.MCELL_2_PROPERTIES_lemma1;; Rogers.XYOFCGX;; searcht 5 [name "CGX"];; searcht 5 [`VX`;`mcell2`];; searcht 5 [name "AJR"];; searcht 5 [`VX V X SUBSET y`];; searcht 5 [`midpoint`;`circumcenter {a,b}`];; searcht 5 [`X SUBSET set_of_list ul`];; searcht 5 [`set_of_list V SUBSET Q`];; searcht 5 [`affine_dependent {a,b}`];; searcht 15 [`set_of_list (truncate_simplex k ul)`];; searcht 15 [`truncate_simplex 1 ul`];; searcht 5 [`stem x = {a,b}`];; searcht 5 [`set_of_list [a;b]`];; searcht 5 [`radV`;`midpoint`];; searcht 5 [`radV`;`dist`];; searcht 5 [`hl [a;b]`];; searcht 5 [`midpoint`;`dist`];; searcht 50 [`VX`];; searcht 5 [`gammaX`;`gamma4fgcy`];; searcht 15 [`permutes`;`hl`];; Pack_defs.mcell3;; Pack_defs.VX;; searcht 15 [`(\(k,u). f k u) (a,b)`];; searcht 15 [name "BETA_PAIR"];; searcht 15 [`(FST x, SND x)`];; Pack_defs.cell_params;; searcht 5 [`mcell4`;`mcell 4`];; searcht 5 [`x INTER x`];; searcht 25 [`(@)`];; searcht 5 [`(?x. P x) ==> (P (@x. P x))`];; searcht 5 [`(A = B) ==> A SUBSET B`];; searcht 5 [`truncate_simplex k X = X`];; (* Jan 1, 2013 *) searc 'a' 0 [`set_of_list`;`FINITE`];; searc 'b' 1 [`CARD`;`LENGTH`;`set_of_list`];; searcht 5 [`CARD B <= CARD A`;`A SUBSET B`;`FINITE`];; searcht 5 [`mcell4`;`convex hull s`];; searcht 5 [`set_of_list ul SUBSET V`;`barV`];; searcht 5 [`set_of_set ul SUBSET mcell4 V ul`];; searcht 5 [`s SUBSET f hull s`];; searcht 5 [`neglibible`;`{}`];; searcht 5 [`VX V X`;`INTER`];; searcht 5 [`CARD`;`barV`];; searc 'c' 2 [`{a,b} = {c,d}`];; Ajripqn.AJRIPQN;; searc 'd' 0 [`set_of_list`;`truncate_simplex`;`SUBSET`];; searc 'e' 5 [`LENGTH`;`truncate_simplex`];; Geomdetail.CARD_SET_OF_LIST_LE;; Marchal_cells_3.BARV_CARD_LEMMA;; searcht 5 [`INSERT`;`set_of_list`];; searcht 5 [`truncate_simplex 2 (CONS x y)`];; searcht 5 [`set_of_list (CONS x y)`];; CARD_CLAUSES;; searcht 5 [`CARD {a,b,c}`];; searcht 5 [`{ x| F}`];; GSPEC_EMPTY;; conj_list;; searcht 5 [`\x. F`];; CONJ;; searcht 5 [`sum {}`];; searcht 5 [`edgeX`;`mcell2`];; searcht 15 [`truncate_simplex 2 ul`];; Marchal_cells.TRUNCATE_SIMPLEX_EXPLICIT_2;; searcht 5 [`LENGTH (truncate_simplex k ul)`];; searcht 5 [`EL k (truncate_simplex r ul)`];; searcht 5 [`edgeX`;`mcell`];; searcht 5 [`CARD {u,v}`];; set_of_list3;; searcht 15 [`truncate_simplex k ul`];; set_of_list3;; searcht 5 [`CARD (X UNION Y)`];; searcht 5 [`CARD {}`];; searcht 5 [`CARD x <= CARD y`;`SUBSET`];; searcht 5 [name "HDT"];; searcht 5 [`set_of_list ul = A INTER B`];; set_of_list4;; searcht 5 [`SUBSET`;`CARD`;`a=b`];; searcht 5 [`CARD`;`edgeX`];; searcht 5[ `CARD {a,b} <= 2`];; searcht 5 [`edgeX`;`mcell4`];; searcht 5 [`CARD`;`barV`];; searcht 5 [`CARD`;`DIFF`];; searcht;; HDTFNFZ_ALT;; Hdtfnfz.HDTFNFZ;; searcht 15 [`BIJ`;`f(g(x))`];; searcht 15 [`sum X f = sum Y f`;`f x = &0`];; searcht 15 [`sum X f = sum X g`];; searcht 5 [`sum s (\x. -- f x)`];; searcht 5 [name"BIJ_SUM"];; (* Jan 2, 2013 *) searcht 5 [`abs x <= abs a + abs b`];; searcht 5 [`abs (x - y) <= abs x + abs y`];; searcht 5 [`abs (x/ y) = abs x / abs y`];; searcht 5 [`x / y <= z / y`];; searcht 5 [`x/y = x * inv y`];; searcht 15 [`x * c <= y * c`];; searcht 5 [`x pow 2 <= y pow 2`];; searcht 5 [`abs (x pow n)`];; searcht 5 [name "HL_2"];; searcht 5 [`dihu2`];; searcht 5 [`dihu3`];; searcht 15 [`gammaX`];; searcht 5 [`permutes`;`barV`;`mcell`];; searcht 5 [`mcell2`;`edgeX`];; searcht 5 [`{a,b} = {c,d}`];; searcht 5 [`permutes`;`INSERT`];; Marchal_cells_3.LEFT_ACTION_LIST_3_EXISTS;; Marchal_cells_3.LEFT_ACTION_LIST_2_EXISTS;; searcht 5 [`p permutes 0..1`;`left_action_list`];; Qzksykg.TWO_REARRANGEMENT_LEMMA;; Rvfxzbu.RVFXZBU;; Qzksykg.QZKSYKG1;; searcht 5 [`edgeX`;`{}`];; searcht 5 [`negligible {}`];; RIJRIED;; searcht 5 [`edgeX`;`mcell3`];; searcht 5 [`CARD {a,b,c}`];; searcht 5 [`CARD`;`DIFF`];; searcht 5 [`CARD {a,b}`];; searcht 5 [`CARD X = 0`];; searcht 5 [`CARD X = 1`];; searcht 5 [`set_of_list (truncate_simplex 2 ul) = x INSERT y`];; searcht 5 [`barV`;`CARD`];; LENGTH4;; set_of_list4;; searcht 15 [`X DIFF e`;`edgeX`];; searcht 5 [`CARD {x,y} = 2`];; searcht 15 [`CARD x = 2`];; searcht 5 [`edgeX`;`mcell k`];; searcht 5 [`hl a < hl b`];; searcht 5 [`truncate_simplex k ul = ul`];; searcht 5 [`truncate_simplex`;`barV`];; searcht 5 [name "CFFO"];; searcht 5 [`EL k (truncate_simplex r ul)`];; searcht 5 [`stem`;`EL`];; searcht 5 [`cc_A0`;`EL`];; searcht 5 [`~(x = {})`;`?`];; searcht 5 [`V INTER X = set_of_list a`];; searcht 5 [`x IN aff_gt u {x}`];; searcht 5 [`leaf V (CONS x y)`];; searcht 15 [`truncate_simplex k vl`;`CONS`];; LENGTH3;; searcht 5 [`LENGTH (truncate_simplex k vl)`];; Marchal_cells.TRUNCATE_SIMPLEX_EXPLICIT_2;; STEM_OF_LEAF;; STEM_OF_LEAF;; searcht 5 [name "CFF"];; searcht 5 [`edgeX`;`cc_cell`];; searcht 5 [`mcell3`;`edgeX`];; searcht 5 [`cc_cell`;`NULLSET`];; searcht 5 [`barV V 3`;`cc_uh`];; searcht 5 [`EL`;`cc_uh`];; searcht 5 [`set_of_list (truncate_simplex k (ul))`];; searcht 15 [`EL k (cc_uh V ul)`];; searcht 15 [`LENGTH (cc_uh V ul)`];; searcht 5 [`CARD`;`barV`];; cc_uh;; Bump.SET_OF_LIST_TRUNCATE_2;; LENGTH3;; set_of_list3;; searcht 5 [`CARD`;`4`;`~(a =b)`];; searcht 5 [`truncate_simplex k ul SUBSET ul`];; searcht 5 [`mcell_set`;`cc_cell`];; searcht 5 [`cc_cell`;`cc_A0`];; searcht 5 [name "FUE"];; searcht 5 [`CONS x y = CONS x' y'`];; ZASUVOR;; FUEIMOV_4;; searcht 5 [`cc_uh V ul = CONS x y`];; searcht 5 [`{a,b} = {c,d}`];; searcht 5 [`cc_uh V ul = CONS x y`];; searcht 5 [`coplanar`;`cc_uh`];; searcht 5 [`coplanar`;`affine hull {a,b,c}`];; searcht 5 [`aff_gt`;`affine hull s`];; searcht 15 [`s IN aff_gt u v`];; SUBSET_HULL;; searcht 15 [`s SUBSET f hull s`];; searcht 15 [`s IN S /\ S SUBSET U`];; (* Jan 3, 2013 *) searc 'a' 1 [`coplanar`;`affine hull s`];; searc 'b' 0 [`aff_dim`;`collinear`];; searcht 5 [`aff_dim`;`INSERT`];; searcht 5 [`aff_dim x <= aff_dim y`;`x = y`];; searcht 5 [`affine hull (affine hull h)`];; searcht 5 [`s SUBSET f hull s`];; searcht 5 [`aff_dim (affine hull s)`];; coplanar;; searc 'c' 1 [`connected`;`segment`];; searcht 25 [`connected`;`open`];; searcht 5 [`a IN segment [a,b]`];; searcht 5 [`wedge_ge`;`wedge`];; searcht 5 [`wedge_ge`];; searcht 35 [`wedge`];; Local_lemmas1.AFF_GE_WEDGE_DISJOINTION;; OPEN_WEDGE;; Local_lemmas1.EDGE_NOT_INTER_WITH_WEDGE;; WEDGE_ALT;; searcht 5 [name "WEDGE_GE_ALMOST"];; WEDGE_GE_ALMOST_DISJOINT ;; (* not loaded in work_in_progress_merge.hl *) COPLANAR_UNION;; CONNECTED_SEGMENT_NOT_COVERED;; searcht NAN [`closed`;`wedge_ge`];; searcht 5 [`mcell`;`convex`];; searcht 5 [def "wedge_ge"];; searcht 55 [def "azim"];; Sphere.AZIM;; azim;; searc 'e' 0 [`wedge_ge`;`aff_ge`];; searcht NAN [`wedge_ge`;name "split"];; searcht 5 [`wedge`;`UNION`];; searc 'd' 1 [`closed`;`aff_ge`];; searcht NAN [`?`;`azim a b c d = e`];; searcht 5 [`wedge_ge`;`azim a b c d = pi`];; searcht 5 [`convex`;`closed`];; searc 'f' [`polyhedron`;`closed`];; searcht 5 [`~(x = {})`;`?`];; searcht 5 [`wedge_ge`;`azim`];; searcht 50 [`collinear`;`azim`];; searcht 5 [`azim a b c d + azim a b d e`];; searc 'g' 0 [`collinear`;`azim`;omit `~`];; searcht 5 [`&0 <= azim a b c d`];; searcht 5 [`open`;`closed`];; searcht 5 [`azim`;`-- x`];; searcht 5 [`azim`;`pi`];; searcht 25 [`conv0`];; searcht 5 [`aff_ge {} {a,b}`];; searcht 5 [`aff_sgn`;`aff_gt`];; searcht 15 [`aff_gt`;`%`];; searcht 15[ `azim`;`&2 * pi`];; searcht 5 [`closed`;` a dot b`];; searcht 5 [`aff_ge`;`closed`];; searcht 5 [`closed (A UNION B)`];; searcht 5 [`NULLSET`;`edgeX`];; searcht 5 [`edgeX V X = {}`];; searcht 5 [`convex`;`mcell`];; searcht 5 [`coplanar`;`SUBSET`];; searcht 5 [`coplanar`;`NULLSET`];; WEDGE_WEDGE_GE;; searcht 5 [`NULLSET `;`UNION`];; searcht 5 [`NULLSET`;`aff_ge`];; Conforming.NEGLIGIBLE_AFF_GE_2_1;; searcht 5 [`collinear`;`leaf`];; searcht 5 [`set_of_list (CONS x y)`];; searcht 5 [`SUBSET`;`negligible`];; searcht 5 [`coplanar`;`SUBSET`];; searcht 5 [`azim`;`aff_ge`];; AZIM_DEGENERATE;; searcht 5 [`wedge_ge`;`azim`];; (* Jan 4, 2012 *) searcht 5 [`((!x. p x) /\ (!x. q x)) <=> R`];; Local_lemmas.AZIM_EQ_0_GE_ALT2;; searc 'r' 0 [`&0 <= azim a b c d`];; searcht 5 [`azim a b c d + azim a b d e`];; searcht 5 [`collinear`;`affine hull {a,b}`];; help_grep "DISJ";; searcht 5 [`collinear`;`~(a = b)`];; searcht 5 [`affine hull s SUBSET aff_ge a b`];; searcht 5 [`DISJOINT`;`collinear`];; bb 15;; COPLANAR_INSERT;; searcht 5 [name "COPLANAR_INSERT"];; searcht 5 [`open`;`wedge`];; searcht 5 [`closed`;`wedge_ge`];; searcht 5 [`open`;`closed`];; searcht 5 [`wedge a b c d SUBSET wedge_ge a b c d`];; searcht 5 [`wedge`;`wedge_ge`];; searcht 5 [`wedge_ge`];; searcht 5 [`segment`;`convex`];; searcht 15 [`aff_ge`;`aff_gt`];; DISJOINT {u, v} {w} Collect_geom.IN_AFF_GE_INTERPRET_TO_AFF_GT_AND_AFF;; searcht 5 [`segment`;`%`];; searcht 5 [`wedge`;`wedge_ge`];; searcht 5 [name "CFF"];; searcht 20 [`coplanar {a,b,c,d}`];; searcht 5 [`coplanar`;`INTER`];; searcht 5 [`s SUBSET f hull s`];; searcht 15 [`aff_dim s <= &2`];; Print_types.print_thm_types Njiutiu.AFF_DEPENDENT_AFF_DIM_4;; searcht 5 [`coplanar`;`aff_dim`];; searcht 5 [`coplanar`;`affine_dependent`];; searcht 15 [`affine_dependent {a,b,c,d}`];; searcht 15 [`affine_dependent`;`sum`];; searcht 15 [`sum (x INSERT y)`];; searcht 5 [`affine hull {a,b}`;`%`];; searcht 5 [`affine hull {a,b,c}`;`%`];; searcht 5 [`a % v = a % u`];; searcht 5 [`a % (b + c)`];; searcht 5 [`a % (b % c)`];; searcht 5 [`aff_ge`;`aff_gt`];; searcht 5 [`collinear`;`DISJOINT`];; searcht 5 [`stem [a;b;c]`];; searcht 5 [`stem`];; CELL_NN;; searcht 5 [`set_of_list [a;b;c]`];; searcht 5 [`aff_gt x y SUBSET affine hull u`];; searcht 5 [`chi_msb ul`;`%`];; searcht 5 [`affine hull s`;`chi_msb`];; CHI_MSB_IMP_COPLANAR;; searcht 15 [`coplanar`;`affine hull s`];; searcht 5 [`aff_dim {a,b,c} <= &2`];; searcht 5 [`aff_dim`;`collinear`];; searcht 5 [`collinear`;`leaf`];; bb 20;; chi_msb_coplanar;; COPLANAR_INSERT;; searcht 5 [`set_of_list ul = {a,b,c}`];; searcht 5 [`azim a b c d = &0`];; searcht 50 [`wedge_ge`;`wedge`;];; searcht 5 [`collinear`;`leaf`];; searcht 5 [`wedge_ge`;`(:real^3)`];; searcht 5 [`aff_ge`;`azim a b c d = &0`];; searcht 5 [`SUBSET`;`negligible`];; searcht 5 [`wedge_ge`];; searcht 15 [`collinear`;`affine hull s`];; searcht 15 [`affine hull s SUBSET aff_ge u v`];; searcht 5 [`DISJOINT`;`collinear`];; Local_lemmas.AZIM_EQ_0_GE_ALT2;; AZIM_BASE_SHIFT_LE;; searcht 5 [`azim a b c c`];; Local_lemmas.AZIM_EQ_0_GE_ALT2;; searcht 5 [`azim a b c d`;`&2 * pi - azim a b c d`];; Rogers.AZIM_COMPL_EXT;; (* Jan 5, 2012 *) searcht 5 [`wedge_ge`];; AZIM_DEGENERATE;; searcht 5 [`&0 <= azim a b c d `];; searcht 5 [`azim a b c d + azim a b d e`];; searcht 5 [`azim a b c d = &0`];; searcht 15 [`wedge_ge`;`wedge`;`aff_ge`];; (* link in Ky's work *) searcht 5 [name "REU"];; searcht 15 [name "Tsk"];; Tskajxy_lemmas.SOL_SOL_Y_EXPLICIT;; Tskajxy_lemmas.DIHX_DIH_Y_lemma;; searcht 5 [name "REU"];; Reuhady.REUHADY1;; searcht 5 [`hl x < hl y`];; searcht 5 [`truncate_simplex k (CONS x y)`];; searcht 5 [`set_of_list [a;b]`];; searcht 5 [`CONS a b = CONS a' b'`];; searcht 5 [`collinear`;`leaf`];; searcht 5 [`set_of_list [u0;u1;u2]`];; searcht 5 [`wedge_ge`;`INTER`;`aff_ge`];; searcht 5 [`collinear`;`~(a = b)`];; searcht 5 [`set_of_list x SUBSET V`;`barV`];; searcht 5 [`azim`;`aff_ge`];; Leaf_cell.FCHKUGT;; TL;; searcht 5 [`aff_gt s t = aff_gt s t'`];; searcht 15 [`aff_gt`;`aff_ge`];; searcht 5 [`DISJOINT`;`collinear`];; searcht 5 [`affine hull {a,b}`;`collinear`];; Pack_defs.mcell_set;; Print_types.print_thm_types;; Tskajxy_lemmas.gammaX_gamma3f;; bb 5;; searcht 5 [`radV`;`eta_y`];; Sphere.packing;; searcht 5 [`dist(a,b) + dist(b,c)`];; bb 4;; searcht 5 [`coplanar`;`collinear`];; searcht 5 [`set_of_list (truncate_simplex 2 ul)`];; searcht 5 [`{}`;`negligible`];; print_proof();; Print_types.print_goal_types();; print_goalstack;; print_proof();; (* Jan 6, 2013 TSKAJXY 1 and 2 cells *) searcht 15 [`mcell1`];; searc 'a' 1 [`mcell1`;`HD`];; searc 'b' 0 [`mcell`;`HD`];; searc 'c' 2 [`edgeX`;`mcell`];; searcht 10 [`gammaX`];; searcht 5 [`gammaX`;`{}`];; searcht 5 [`total_solid`];; searcht 5 [`sum {x}`];; searc 'h' 1 [`a SUBSET b /\ b SUBSET a`];; searcht 25 [`VX V`];; searc 'd' 0 [`{}`;`negligible`];; searc 'e' 0 [`VX V X = {}`];; searcht 5 [`edgeX V X = {}`];; searcht 5 [`NULLSET`;`vol`];; searc 'f' 0 [`set_of_list ul SUBSET V`;`barV`];; searcht 15 [`set_of_list ul = x INSERT y `];; searcht 5 [`mcell2`;`VX`];; searcht 5 [`mcell2`;`edgeX`];; searcht 15 [`mcell`;`barV`;`V INTER X`];; searcht 15 [`set_of_list (truncate_simplex 1 ul)`];; update_database();; Sphere.BARV;; searcht 4 [`CARD`;`barV`];; searc 'g' 1 [`CARD X = 4`;`~(x = y)`];; searcht 5 [`set_of_list ul`;`4`];; searcht 5 [`sum {a,b}`];; searc 'i' 0 [name "BETA_PAIR"];; searcht 5 [`set_of_list [a;b]`];; searcht 5 [`dihX`];; searcht 5 [`mcell2`;`VX`];; searcht 15 [`radial`];; searcht 15 [`radial_norm`];; searcht 15 [`eventually_radial`];; searcht 15 [def "eventually"];; searc 'j' 0 [`radial_norm`;`DIFF`];; searcht 5 [`radial_norm`;`INTER`];; searcht 5 [def "rcone"];; searcht 5 [`radial_norm`;`rcone_lt`];; searcht 500 [name "Vol1.";`sol`];; searcht 5 [`solid_triangle`];; searcht 15 [`conic_cap`];; searc 'k' 0 [`eventually_radial`;`mcell`];; Urrphbz2.URRPHBZ2;; Urrphbz2.EVENTUALLY_RADIAL_RCONE_GE_ABC_A;; searcht 5 [name "Count";`rcone_gt`];; Sphere.rcone_gt;; searcht 5 [`rcone_ge`;`dot`];; searcht 5 [`&0 < dist (p,q)`];; Print_types.print_thm_types DIST_NZ;; DIST_NZ;; type_of `radial_norm`;; searcht 15 [`convex hull s`;`INTERS`];; searcht 15 [`aff_ge s t INTER aff_ge s' t'`];; Cfyxfty.inter_aff_ge_3_1_is_aff_ge_1_3;; (* ! *) Collect_geom2.ARIKWRQ;; searcht 5 [`&0 <= dist(a,b)`];; searcht 5 [`dist (p,x ) <= dist (p,y)`;`dot`];; searcht 5 [`dist (x,y) pow 2`;`dot`];; searcht 5 [`norm = r`;`NULLSET`];; searcht 5 [name "OWCZKJR"];; type_of `radial_norm`;; radial_norm;; searcht 5 [`normball`;`dist (y,x) < u`];; searcht 5 [def "normball"];; searcht 5 [`sphere`;`NULLSET`];; searcht 5 [`eventually_radial_norm`;`eventually_radial`];; List.length(searcht 500 [`radial_norm`]);; (* 37 *) hd (definitions());; searchl (map (fun t -> ("",t)) (definitions())) [`radial_norm`];; type_of `eventually_radial_norm`;; Vol1.eventually_radial_norm;; searcht 15 [def "^sol$"];; searcht 5 [`sol`;`measurable`;`INTER`;`normball`];; Vol1.pre_def_4_3b;; open Vol1;; radial_normball;; Vol1.sol;; searcht 50 [`rect`];; searcht 50 [`volume_prop_fix`];; searcht 50 [`primitive`];; searcht 50 [`ellipsoid`];; searcht 50 [`hinhcau`];; Vol1.hinhcau;; searcht 50 [`map0`];; DISJOINT;; INTER_ACI;; nonempty_cube;; Vol1.sol_spec;; (* Jan 7, 2013 *) searcht 5 [`vol X = vol Y`];; searcht 5 [`measurable`;`mcell`];; volume_props;; searcht 5 [`sphere`];; searcht 5 [`measurable (X INTER Y)`];; searcht 5 [`measurable (ball (x,r))`];; searcht 1 [`SDIFF`;`vol`];; searcht 5 [`NULLSET`;`UNION`];; searcht 5 [`negligible {}`];; print_proof();; type_of `sphere`;; searcht 5 [`sphere`];; NEGLIGIBLE_SPHERE;; searc 'a' 0 [`negligible`;`SUBSET`];; searcht NAN [`sol`;`INTER`;`ball`];; searcht 50 [`sol`];; searcht 5 [`mcell`;`eventually_radial`];; searcht 5 [`set_of_list ul SUBSET V`;`barV`];; searcht 20 [`set_of_list ul = x INSERT y`];; searc 'b' 0 [`radial_norm`;`x < t`;`==>`];; searcht 5 [`radial_norm`;`radial`];; Vol1.sol;; searcht 5 [`(X INTER Y) INTER Z`;`X INTER Y INTER Z`];; Cfyxfty.inter_aff_ge_3_1_is_aff_ge_1_3;; (* ! *) Collect_geom2.ARIKWRQ;; searcht 5 [`aff_ge`;`convex hull s`];; searcht 25 [def "^conv"];; searcht 5 [`conv`;`affsign`];; searcht 5 [`aff_ge`;`affsign`];; searcht 5 [`coplanar`;`coplanar_alt`];; searcht 5 [name "MCELL2_VX_PROPS"];; searcht 5 [`coplanar`;`CARD`];; searcht 5 [`CARD {a,b,c,d}`;`~(a = b)`];; print_proof();; searcht 50 [`rogers`];; searcht 5 [`aff `;`rogers`];; searcht 5 [`omega_list_n`;`aff`];; searcht 50 [`aff`];; searcht 5 [name "COMPATIBLE_BW_TWO_LEMMAS2"];; type_of `hypermap`;; type_of `HYP`;; searcht 5 [`coplanar`;`coplanar_alt`];; (* Jan 18, 2013 *) (* TSK_in_progress *) searcht 5 [`norm`;`dist`];; searcht 5 [`norm (a % b)`];; searcht 5 [`aff_ge {a} {b,c,d}`;`%`];; searcht 5 [`DISJOINT`;`coplanar`];; searcht 15 [`convex`;`%`;`INSERT`;`{a,b,c,d}`];; searcht 5 [def "bis"];; searcht 100 [`omega_list_n`];; searcht 100 [`omega_list`];; searcht 5 [`coplanar`;`omega_list_n`];; searcht 5 [`omega_list_n`;`aff_dim`];; searcht 5 [`negligible`;`aff_dim`];; searcht 5 [`mcell1`;`rogers`];; searcht 5 [`SUBSET`;`negligible`];; searcht 5 [`convex`;`rogers`;`omega_list_n`];; Marchal_cells.OMEGA_LIST_0_EXPLICIT;; searcht 15 [`omega_list`;`HD`];; searcht 5 [`omega_list_n`];; searcht 5 [`omega_list_n V ul 0`];; searcht 5 [`NULLSET`;`affine hull s`];; searcht 5 [`coplanar`;`affine hull s`];; searcht 5 [`convex hull s SUBSET affine hull s`];; searcht 5 [`f hull s SUBSET f hull t`];; searcht 5 [`affine hull (affine hull x)`];; searcht 5 [`aff_ge {a,b,c} {d}`;`%`];; searcht 5 [`DISJOINT a b = DISJOINT b a`];; searcht 5 [`dot`;`dist(a,b) <= dist(c,d)`];; searc 'a' 1 [`convex`;`a dot b`];; searcht 8 [`convex`;`%`;`vsum`];; searcht 5 [`vsum`;`{a,b,c,d}`];; searcht 15 [`sum (i..k)`;`SUC`];; searcht 5 [`convex`;`%`;`&1`;omit `vsum`];; Leaf_cell.DIST_LE_HALF_PLANE;; searcht 5 [`voronoi_list`;`omega_list_n`];; searcht 5 [`voronoi_list`;`dist (a,b)`];; searcht 5 [`set_of_list(truncate_simplex k ul)`];; searcht 5 [`barV`;`truncate_simplex`];; searcht 5 [`dist(a,b) = dist(c,d)`;`dot`];; searcht 5 [`&0 <= dist(x,y)`];; searcht 25 [`~coplanar {(a:real^3),b,c,d}`;`%`;`&1`];; searcht 15 [`affine hull s`;`(:real^A)`];; searcht 5 [`coplanar`;`aff_dim`];; searcht 5 [`aff_dim`;`dimindex`];; searcht 5 [`affine hull {a,b,c,d}`;`%`];; searcht 15 [`&0 <= a * b`;`&0 < x`];; searcht 15 [`dot`;`dist(a,b) < dist(c,d)`];; searcht 5 [`&0 < dist (x,y)`];; searcht 15 [`barV`;`~(x = y)`];; Sphere.BARV;; searcht 5 [def "voronoi_nondg"];; searcht 5 [`voronoi_nondg`];; searcht 5 [`voronoi_list`;`aff_dim`];; Sphere.VORONOI_LIST;; searcht 5 [`initial_sublist ul ul`];; searcht 5 [`barV`;`truncate_simplex`];; searcht 5 [`truncate_simplex 0`];; searcht 15 [`set_of_list`;`LENGTH`];; searcht 15 [`set_of_list`;`CONS x y`];; searcht 5 [`barV`;`truncate_simplex`];; searcht 5 [`EL`;`truncate_simplex`];; searcht 5 [`mcell1`;`cball`];; searcht 5 [`ball`;`cball`;`SUBSET`];; searcht 5 [`(X DIFF Y) INTER Z`;`(X INTER Y) DIFF Z`];; Pack_defs.mcell1;; searcht 5 [`rcone_gt`;`dot`];; searcht 30 [`rcone_gt`];; RCONE_GT_HYPERPLANE;; searcht 5 [`a % b dot c`];; searcht 5 [`a % b % c`];; searcht 5 [`rogers`;`{a,b,c,d}`;`convex`];; searcht 5 [`hl [a;b]`];; searcht 15 [`truncate_simplex k`;`CONS`];; searcht 5 [`barV`;`CONS`;`EL`];; searcht 5 [name "LENGTH4"];; searcht 5 [`radial`;`sol`];; searcht 5 [` A INTER A`];; searcht 5 [`measurable`;`ball`];; searcht 5 [`measurable`;`mcell`];; searcht 5 [`mcell`;`mcell1`];; searcht 5 [`sqrt x = &0`];; searcht 5 [`gammaX`];; searcht 5 [`gammaX`];; searcht 5 [`&0 <= sol a b`];; searcht 5 [`pow`;`mm1`];; searcht 5 [`&0 <= vol X`];; searcht 5 [`vol X >= &0`];; searcht 15 [`&0 <= x * y`];; searcht 5 [`sqrt x pow n`];; searcht 5 [`sqrt x pow 2`];; searcht 5 [def "mxi"];; (* Jan 20 *) print_proof();; GAMMAX_MCELL2;; Pack_defs.dihX;; Pack_defs.dihu2;; searcht 5 [`cell_params_d`];; searcht 5 [`cell_params`];; searcht 25 [`initial_sublist`];; searcht 15 [`CONS`;`LENGTH`];; LENGTH4;; searcht 30 [`APPEND`];; searcht 5 [name "AJR"];; searcht 5 [`omega_list_n`;`permutes`];; Marchal_cells_2_new.LEFT_ACTION_LIST_1_PROPERTIES;; Bump.BETA_ORDERED_PAIR_THM;; searcht 5 [`mxi V ul = mxi V vl`];; Marchal_cells_3.MCELL_ID_MXI_2;; searcht 15 [`omega_list_n V ul k = omega_list_n V vl k`];; Marchal_cells_3.MCELL_ID_OMEGA_LIST_N;; searcht 5 [`CONS x y = CONS x' y'`];; searcht 5 [`measure X + measure Y`];; searcht 5 [`bis_le`;`bis`];; searc 'a' 0 [`negligible`;`dot`];; DOT_RMUL;; searcht 5 [`measurable`;`dist`];; searc 'e' 1 [`measurable`;`convex`;`bounded`];; searc 'b' 0 [`convex`;`mcell`];; searc 'c' 0 [`bounded`;`mcell`];; searc 'd' 0 [`convex`;`bis_le`];; searcht 5 [`negligible`;`SUBSET`];; searcht 5 [`a % v = vec 0`];; searcht 5 [`mcell2`;`rcone_ge`];; searcht 5 [`negligible {}`];; searcht 5 [`~ ~ x`];; searcht 5 [`frustum`];; searcht 15 [`frustt`];; VOLUME_FRUSTT_WEDGE;; searcht 5 [def "^wedge"];; RCONE_GT_HYPERPLANE;; searcht 8 [`rcone_ge`;`dot`];; RCONE_GE;; searcht 5 [`dot`;`dist(a,b) <= dist(c,d)`];; searcht 5 [`dist(x,y) = &0`];; searcht 5 [name "Cou";`ball`];; DIST_NZ;; searcht 5 [`norm`;`dot`];; searcht 15 [`x pow 2 <= y pow 2`];; searcht 15 [`atn2`;`ups_x`];; Sphere.arclength;; searcht 5 [`arcV`;`dot`];; Trigonometry1.DOT_COS;; searcht 5 [`arclength`;`arcV`];; Trigonometry1.arcVarc;; searcht 5 [`cos`;`rcone_ge`];; searcht 5 [`arcV a b c = arcV a c b`];; searcht 5 [`arcV u u v`];; searcht 5 [`(v:real^A) - v`];; searcht 5 [`norm (vec 0)`];; searcht 5 [`norm x = &0`];; searcht 15 [`&0 <= x * y <=> &0 <= y`];; searcht 5 [`&0 < norm x`];; searcht 5 [`arcV a b c = arcV a' b' c'`];; searcht 5 [`arcV v u u`];; searcht 5 [`cos (&0)`];; searcht 5 [`arcV`;`pi`];; Local_lemmas1.ARCV_BOUNDS;; searcht 5 [`cos x <= cos y`];; searcht 5 [`atn2 (&0,y)`];; searcht 5 [`ups_x a b c = ups_x a' b' c'`];; searcht 5 [`atn2 (x,y) <= atn2(x',y')`];; searcht 17 [`arcV`;`cos`];; searcht 5 [`&0 < dist(a,b)`];; searcht 5 [`&0 <= ups_x a b c`];; searcht 5 [`atn2(x, -- y)`];; searcht 5 [`atn`;`atn2`];; searcht 15 [`atn(x / y)`];; searcht 5 [`x / (--u)`];; searcht 5 [`inv (--x)`];; searcht 5 [`a pow 2 <= b pow 2`];; searcht 5 [`atn x <= atn y`];; searcht 5 [`x pow 2`;`x * x`];; searcht 5 [`frustt`;`vol`];; searcht 5 [`frustum`];; type_of `dihV`;; searcht 5 [`bis_le`;`dot`];; searcht 5 [`SDIFF`];; searcht 5 [`NULLSET`;`sphere`];; searcht 5 [`circular_cone`];; searcht 5 [`c_cone`];; searcht 5 [`rcone_ge`;`rcone_gt`];; searcht 5 [`SDIFF`];; searcht 5 [`negligible {}`];; searcht 15 [`rcone_ge`;`rcone_gt`];; searcht 5 [`?(u,v). p`];; searc 'k' 0 [`negligible`;`dot`];; searcht 5 [`vol`;`rcone_ge`];; searcht 5 [`SDIFF`;`measurable`];; searcht 15 [`measure X = measure Y`];; searcht 5 [`measurable`;`rcone_ge`];; searcht 5 [`wedge`;`wedge_ge`];; searcht 5 [`affine`;`NULLSET`];; searcht 5 [`aff_ge s t SUBSET affine hull t'`];; searcht 5 [`(A UNION B) SUBSET (A' UNION B')`];; searcht 5 [`aff_ge`;`wedge_ge`];; searcht 5 [`dihV a b c d <= pi`];; searcht 5 [`dihV a b c d = pi`];; searcht 5 [`coplanar`;`mxi`];; searcht 2 [`coplanar`;`NULLSET`];; searcht 5 [`coplanar`;`affine hull s`];; searcht 5 [`collinear`;`coplanar`];; SET_RULE;; searcht 15 [`azim`;`dihV`];; searcht 5 [`azim a b c d`;`&2 * pi`];; searc 'l' 2 [`{a,b} = {c,d}`];; searc 'm' 1 [`&0 < hl u`];; searcht 5 [`sqrt2 * sqrt2`];; searcht 1 [`SDIFF`;`vol X = vol Y`];; searcht 5 [`measurable`;`mcell2`];; searcht 1 [`measurable`;`frustt`;`wedge`];; searcht 5 [`bis_le`;`dot`];; searcht 5 [`norm`;`pow`;`dot`];; searcht 5 [`a dot a - b dot b`];; searcht 5 [`(a + b) dot c`];; searcht 5 [`hl`;`dist`];; searcht 5 [`SDIFF`;`mcell2`];; FRUSTT_WEDGE_RCONE_GE;; MCELL2_SPLIT;; searcht 5 [`wedge_ge`;`aff_ge`];; searcht 5 [`mcell2`;`rcone_ge`];; searcht 5 [`SDIFF X Y = SDIFF Y X`];; searcht 5 [`&0 < hl(truncate_simplex 1 ul)`];; searcht 5 [def "gamma2_x_div_azim"];; searcht 5 [def "^lmfun"];; searcht 5 [`gamma2_x_div_azim`;`lfun`;`sqrt`];; Pack_defs.mcell2;; (* Jan 22, 2013 *) searcht 5 [`vol X = vol Y + vol Z`;`mcell2`];; searcht 5 [`p permutes 0..1`];; Marchal_cells_2_new.LEFT_ACTION_LIST_1_PROPERTIES;; searcht 5 [`permutes`;`left_action_list`;`mcell i j k = mcell i' j' k'`];; searcht 3 [`truncate_simplex`;`permutes`];; searcht 5 [`set_of_list`;`truncate_simplex`];; searcht 5 [`dihV a b c d = dihV b a c d`];; searcht 5 [`sol`;`mcell2`];; searc 't' 0 [`eventually_radial`;`mcell`];; searcht 5 [def"^radial"];; searcht 5 [`radial`;`sol`];; searcht 15 [`dist`;`hl`];; VOLUME_FRUSTT_WEDGE;; searcht 15 [`conic_cap`;`vol`];; (* Jan 23, 2013 *) MCELL2_VX_PROPS;; searcht 5 [`VX`;`V INTER X`];; searcht 5 [`eventually_radial`;`sol`];; searcht 5 [`radial_norm`;`r' <= r`];; searcht 5 [`radial`;`radial_norm`];; searcht 5 [`normball`;`ball`];; Marchal_cells_2_new.RADIAL_VS_RADIAL_NORM;; RADIAL_LE;; searcht 5 [`sol`;`radial`];; searcht 5 [`measurable`;`mcell`];; Sphere.bis_le;; Reuhady.VOLUME_CONIC_CAP_WEDGE_GE_VS_CONIC_CAP;; searcht 5 [`vol X = vol Y`];; searcht 5 [`measurable`;`wedge`];; searcht 5 [`SDIFF`;`rcone_ge`];; searcht 5 [`h / a < t`];; searcht 5 [`SDIFF`;`X INTER Y`];; bb 10;; searcht 5 [`dist a < dist b`;`dot`];; searcht 5 [`mcell2`;`bis_le`];; searcht 5 [`wedge_ge`;`aff_ge`];; searcht 5 [`vol`;`mcell2`];; searcht 5 [`hl(truncate_simplex 1 ul) = hl(truncate_simplex 1 vl)`];; searcht 5 [`dihV a b c d = dihV b a c d`];; searcht 5 [`dihX V X`;`dihV`];; searcht 5 [`dihV`;`dih_y`];; searcht 5 [`gamma2_x_div_azim`];; searcht 5 [`truncate_simplex`;`CONS`];; searcht 2 [`lmfun`;`h0cut`];; searcht 5 [`sqrt8`;`sqrt2`];; searcht 5 [`sqrt(x) = &0`];; searcht 15 [`gamma2_x_div_azim`];; searcht 5 [name "BALL_DIFF_RCONE_GE"];; (* Jan 24, 2013 *) searcht 5 [`&0 <= a`;`dih_x`];; searcht 5 [`&0 <= dihV a b c d`];; searcht 5 [`gamma2_x_div_azim_v2`;`ineq`];; searcht 5 [`sqrt8`;`sqrt2`];; searcht 5 [`mcell1`;name "TSK"];; (* Jan 25, 2013 *) Counting_spheres.POLY_SORT_BIJ;; Counting_spheres.WEDGE_ORDER_DISJOINT;; Counting_spheres.PREIMAGE_BIJ;; Counting_spheres.ORDER_AZIM_SUM2Pi;; TOPOLOGICAL_SORT;; searcht 25 [name "SORT"];; searcht 5 [name "EL_EXPLICIT"];; searcht 5 [name "aff"];; searcht 5 [name "FCHK"];; searcht 5 [`azim`;`aff_ge`];; searcht 5 [`s_leaf`];; searcht 5 [`leaf`;`collinear`];; searcht 5 [`set_of_list (CONS x y)`];; searcht 15 [`azim a b c d = azim a b c d'`];; searcht 5 [`aff_gt s t = aff_gt s {y}`];; searcht 5 [`(i + j) MOD n`];; searcht 5 [`i MOD n = i`];; searcht 5 [`(x MOD n) < n`];; DIVISION;; type_of `PRE`;; type_of `min:num->num->bool`;; searcht 25 [`?(x:num). P x`;`x <= (y:num)`];; Print_types.print_thm_types UPPER_BOUND_FINITE_SET;; searcht 50 [name "MAX";`x:num`];; ;`(x:num) IN s`];; searcht 15 [`x:(num->bool)->num`];; type_of`min_num`;; searcht 15 [`min_num`];; searcht 15 [`wedge`;`wedge_ge`;`mcell_set`];; Leaf_cell.BDXKHTW;; Leaf_cell.EWYBJUA;; searcht 25 [`azim a b c d = &0`;omit `wedge`;omit `wedge_ge`;omit `aff_ge`];; searcht 5 [`azim a b c d + azim a b c' d'`];; searcht 5 [`wedge`;`azim`];; searcht 5 [`azim a b c c`];; searcht 5 [`&0 <= azim a b c d`];; searcht 5 [`azim a b c d = &0`;`aff_ge`];; searcht 5 [`aff_ge s t SUBSET affine hull t'`];; searcht 5 [`negligible`;`affine hull {a,b,c}`];; searcht 5 [`a /\ (?x. P x)`];; (* Jan 26, 2013 *) searcht 5 [`barV`;`FINITE`];; searcht 5 [`packing`;`FINITE`];; searcht 5 [`barV`;`ball`];; searcht 5 [`set_of_list ul SUBSET V`;`barV`];; Packing3.BARV_SUBSET;; searcht 5 [`set_of_list`;`CONS`];; searcht 5 [`hl`;`dist pr`];; DIST_SYM;; Qzyzmjc.BARV_3_IMP_FINITE_lemma2;; SUBSET_UNIONS;; IN_UNIONS;; searcht 5 [`negligible`;`UNIONS`];; searcht 5 [`NULLSET`;`aff_ge`];; searcht 5 [`NULLSET`;`affine`];; searcht 5 [`aff_ge`;`affine hull (s UNION t)`];; searcht 5 [`aff_ge {a,b} {c}`;`collinear`];; Local_lemmas.AZIM_EQ_0_GE_ALT2;; searcht 5 [`wedge_ge a b c d SUBSET X`;`aff_ge`];; searcht 5 [`collinear`;`s_leaf`];; searcht 5 [name "OXL"];; searcht 5 [`sum X f = &0`];; searcht 5 [name "TSK"];; searcht 5 [`beta_bump_v1`];; searcht 5 [`critical_weight`;`&0 <= x`];; searcht 5 [`0 <= CARD X`];; searcht 5 [`;; Leaf_cell.BDXKHTW;; searcht 5 [`s_leaf`;`leaf`];; searcht 5 [`collinear`;`leaf`];; searcht 5 [`azim a b c d = &0`;`aff_ge`];; searcht 5 [`periodic`];; searcht 50 [`azim a b w w' = &0`];; searcht 15 [`azim a b c d + azim a b d e`];; searcht 5 [`&0 <= azim a b c d`];; searcht 5 [`periodic `;`MOD`];; searcht 5 [`((a ==> b ) /\ (b ==> a))`];; searcht 5 [`i MOD n < n`];; searcht 15 [`(a + b) MOD n`];; searcht 5[`wedeg`;`wedge_ge`;`DIFF`];; searcht 5 [`a MOD n = b MOD n`;`a < n`];; searcht 5 [`0 MOD n`];; DIVISION;; searcht 15 [`a MOD n = a`];; searcht 5 [`wedge_ge`;`azim`];; Local_lemmas.AZIM_EQ_0_GE_ALT2;; searcht 5 [`wedge`;`azim`];; searcht 5 [`azim a b c d - azim a' b' c' d' = azim a'' b'' c'' d'' - azim a''' b''' c''' d'''`];; searcht 15 [`collinear`;`aff`];; searcht 15 [`collinear`;`affine hull s`];; COLLINEAR_3_AFFINE_HULL;; searcht 5 [`collinear`;`~(a = b)`];; searcht 5 [`affine hull s SUBSET aff_ge s' t'`];; searcht 5 [`DISJOINT`;`collinear {a,b,c}`];; bb 3;; searcht 5 [`azim a b c d = &0 <=> p`];; searcht 5 [`azim a b c d = &0`;`aff_ge`];; searcht 5 [name "REUH"];; Oxl_def.periodic_mod;; searcht 5 [`azim a b c c `];; searcht 5 [`sum`;`azim`;`&2 * pi`];; searcht 5 [name "GRUT"];; searcht 15 [`sum X (\i. sum Y f)`];; searcht 5 [`FINITE {i | (i:num) < n}`];; searcht 5 [`FINITE`;`mcell_set`];; searcht 5 [`preimage`;`BIJ`];; searcht 5 [`a,b = a',b'`];; MCELL_WEDGE_UNIQUE;; searcht 5 [`edgeX`;`NULLSET`];; Bump.RIJRIED;; searcht 5 [`BIJ`;`sum`];; searcht 5 [name "BETA"];; searcht 5 [`collinear`;`~(a = b)`];; searcht 5[`hplus`;`hminus`];; searcht 5 [`periodic`;`leaf_rank`];; (* Jan 28, 2013 *) searcht 5 [`beta_bumpA_y`];; Counting_spheres.ORDER_AZIM_SUM2Pi;; searcht 5 [`sum x f = sum x f'`];; searcht 5 [`collinear`;`leaf_rank`];; (* Jan 30, 2013 *) searcht 5 [`mcell4`;`leaf`];; searcht 5 [`mcell`;`leaf`];; searcht 15 [`cc_cell`;`leaf`];; searcht 5 [`hl`;`radV`];; searcht 15 [`radV`;`eta_y`];; searcht 5 [`dist`;`d3`];; searcht 15 [`hl`;`dist`];; searcht 15 [`hl a < hl b`];; searcht 15 [`hl a <= hl b`];; searc 'a' 0 [`radV a <= radV b`];; searcht 5 [`affine_dependent`;`collinear`];; searcht 5 [`radV {a,b}`];; searcht 5 [`hl [a;b]`];; Pack_defs.HL;; Marchal_cells_3.HL_2;; searcht 5 [`eta_y a b c = eta_y a b' c'`];; searcht 5 [`&0 <= ups_x a b c`];; searcht 5 [`x pow 2`;`x*x`];; searcht 5 [`&0 <= eta_y a b c`];; searcht 5 [`ups_x a b c = ups_x a c b`];; searcht 5 [`x pow 2 <= y pow 2`];; Sphere.BARV;; searcht 5 [`barV`;`X SUBSET V`];; searcht 5 [`collinear`;`leaf`];; searcht 5 [`collinear `;`~(a = b)`];; searcht 5 [`NULLSET`;`edgeX`];; searcht 15 [`dihX`;`NULLSET`];; searcht 15 [`dihX`;`dihV`];; searcht 50 [`dihX`];; searcht 50 [`dihu4`];; searcht 50 [`mcell2`;`aff_ge`];; searcht 5 [`mcell2`;`dihX`];; searcht 5 [`&0 <= dihV a b c d`];; searcht 5 [`dihV a b c d = &0`];; searcht 5 [`collinear`;`mxi`];; searcht 5 [`collinear`;`omega_list_n`];; searcht 5 [`coplanar`;`collinear`];; searcht 5 [`NULLSET`;`coplanar`];; searcht 5 [`coplanar`;`affine hull s`];; searcht 5 [`aff_ge s t SUBSET affine hull s'`];; searcht 5 [`dihX`;`COND`];; searcht 5 [`dihu3`];; searcht 5 [`FST`;`cell_params_d`];; searcht 5 [`mcell i V ul = mcell i V ul'`];; searcht 15 [`initial_sublist`];; searcht 5 [`barV`;`LENGTH`];; searcht 5 [`SND`;`cell_params_d`];; searcht 5 [`mcell3`;`convex`];; Pack_defs.mcell3;; searcht 15 [`initial_sublist`];; searcht 5 [`APPEND (CONS x y)`];; searcht 5 [`((a ==> b) /\ (b ==> a))`];; searcht 5 [`convex hull s = convex hull y`];; searcht 5 [`set_of_list (truncate_simplex 2 ul)`];; searcht 5 [`affine_dependent`;`NULLSET`];; searcht 5 [`affine_dependent`;`aff_dim`];; searcht 5 [`CARD`;`mxi`];; searcht 5 [`mcell 3`;`cc_cell`];; searcht 15 [`coplanar`;`hull`];; searcht 5 [`affine hull (convex hull s)`];; searcht 5 [`FINITE`;`INSERT`];; searcht 5 [`aff_dim`;`coplanar`];; searcht 5 [`aff_dim`;`DIMINDEX`];; searcht 5 [`coplanar (convex hull s)`];; searcht 25 [`CARD`;`4`];; searcht 5 [`dihV a b c d = dihV a b d c`];; DIHV_SYM;; MCELL2_DIHX_POS;; searcht 5 [`mcell4`;`edgeX`];; (* Jan 31, 2013 *) searcht 5 [`barV`;`mcell4`;`leaf`];; Leaf_cell.RBUTTCS;; searcht 5 [`mcell4`;`convex`];; searcht 5 [`barV V`;`truncate_simplex`];; searcht 5 [`truncate_simplex 2`];; searcht 5 [`hl s <= hl t`];; searcht 15 [`permutes`;`left_action_list`;`?`];; Marchal_cells_3.LEFT_ACTION_LIST_3_EXISTS;; searcht 5 [`CARD`;`mcell4`];; Collect_geom2.NOT_COPLANAR_IMP_CARD4;; Bump.LENGTH4;; searcht 15 [`set_of_list`;`LENGTH`];; searcht 5 [`barV`;`LENGTH`];; searcht 5 [`mcell i V ul = mcell i' V ul'`];; Rvfxzbu.RVFXZBU;; searcht 5 [`barV`;`left_action_list`];; searcht 15 [`CARD`;`2`];; Hypermap.CARD_TWO_ELEMENTS;; searcht 5 [`CARD x <= CARD y`;`SUBSET`];; searcht 5 [`CARD`;`4`;`~(x = y)`];; Marchal_cells_2_new.CARD4_IMP_DISTINCT;; searcht 5 [`a = b ==> b = a`];; searcht 5 [`FINITE`;`s_leaf`];; searcht 3 [`edgeX`;`cc_cell`];; searcht 5 [`cc_cell`;`cc_ke`];; searcht 5 [`mcell4`;`edgeX`];; searcht 5 [`u IN p hull s`];; searcht 5 [`u IN aff_gt s t`];; searcht 10 [`mcell i V ul = mcell i' V ul'`];; searcht 5 [`barV`;`cc_uh`];; searcht 5 [`cc_ke`;`4`];; searcht 5 [`leaf V a ==> leaf V b`];; Leaf_cell.cc_uh;; searcht 5 [`wedge_ge`;`wedge`;`aff_ge`];; searcht 5 [`collinear`;`leaf_rank`];; Print_types.print_goal_types();; searcht 50 [`leaf_rank`;`periodic`];; searcht 5 [`j MOD n < n`];; searcht 5 [`periodic`;`MOD`];; searcht 5 [`wedge`;`azim`];; searcht 5 [`azim a b c c `];; searcht 5 [name "SHIFT";`azim a b c d - azim a' b' c' d'`];; searcht 8 [`azim a b c d + azim a b d e`;omit `pi`];; print_proof();; (* Feb 1, 2013 *) searcht 5 [`azim`;`wedge_ge`];; searcht 5 [`wedge_ge`;`DIFF`];; GSYM Leaf_cell.WEDGE_COMPLEMENT;; searcht 5 [`azim a b c d = &0`];; searcht 5 [`azim a b c d`;`&2 * pi`];; searcht 5 [`mcell4`;`convex`];; searcht 5 [`{a,b} = {c,d}`;`~(a = b)`];; searcht 5 [`CARD`;`mcell4`];; searcht 5 [`CARD`;`4`;`~(a = b)`];; MCELL4_LEAF2;; searcht 5 [`x IN convex hull s`];; searcht 5 [`chi_msb`;`sin`];; searcht 5 [`sin`;`azim`];; searcht 5 [`aff_ge`;`wedge_ge`];; searcht 5 [`convex hull s SUBSET aff_ge a b`];; searcht 5 [`azim a b c d = pi`;`coplanar`];; searcht 5 [`leaf_rank`;`collinear`];; searcht 5 [`coplanar (convex hull s)`];; searcht 5 [`coplanar`;`NULLSET`];; searcht 5 [`azim a b c d + azim a b d c`];; searcht 5 [`wedge_ge a b c d INTER wedge_ge a b c' d'`];; searcht 5 [`NULLSET`;`aff_ge`];; searcht 5 [`aff_ge s t SUBSET affine hull s'`];; searcht 5 [`azim`;`dihV`];; searcht 5 [`dihX`;`dihV`];; searcht 5 [`dihX`;`mcell 4`];; Tskajxy_lemmas.DIHX_DIH_Y_lemma;; searcht 5 [`dihV`;`dih_y`];; searcht 5 [`CARD`;`4`;`mcell4`];; searcht 5 [`barV`;`left_action_list`];; searcht 5 [`mcell j V ul = mcell i V ul'`];; searcht 5 [`barV`;`LENGTH`];; MCELL4_BARV_FI;; searcht 5 [name "S_LEAF_COLLINEAR"];; searcht 5 [`packing V /\ saturated V /\ leaf_rank V ul w0 n f ==> ~collinear {EL 0 ul, EL 1 ul, f k}`];; searcht 5 [`mcell`;`?`;`4`];; searcht 5 [`edgeX V X = {}`];; searcht 5 [`edgeX`;`NULLSET`];; Bump.RIJRIED;; searcht 5 [`leaf_rank`;`CARD`];; searcht 5 [`s_leaf`;`FINITE`];; searcht 5 [`leaf_rank`;name "INJ"];; searcht 5 [`periodic`;`IMAGE`];; searcht 5 [`periodic`;`MOD`];; searcht 5 [`BIJ`;`CARD`];; searcht 5 [`{i | i < n}`;`HAS_SIZE`];; searcht 5 [`i<(n:num)`;`FINITE`];; searcht 5 [`u MOD n = u`];; GSYM MOD_LT;; searcht 5 [`sum s f <= sum s' f`;`SUBSET`];; searcht 5 [`mcell_set`;`FINITE`];; searcht 5 [`mcell4`;`edgeX`];; searcht 5 [`CARD`;`4`;`barV`];; searcht 5 [`set_of_list`;`LENGTH`;`4`];; searcht 5 [`&0 <= dihX V x u`];; searcht 5 [`sum {a,b}`];; searcht 5 [`mcell2`;`edgeX`];; type_of `gg_mcell`;; searcht 5 [`gg_mcell`];; searcht 5 [`sum {X}`];; print_proof();; update_database();; (* Feb 2, 2013 *) searcht 10 [`EL`;`cc_uh`];; searcht 5 [`leaf`;`leaf_rank`];; searcht 5 [`leaf`;`s_leaf`];; searcht 15 [`s_leaf`;`leaf_rank`];; searcht 5 [`{a,b} = {c,d}`];; searcht 5 [`leaf V a ==> leaf V b`];; Leaf_cell.ZASUVOR;; MCELL_IN_WEDGE;; searcht 5 [`s_leaf`;`HAS_SIZE`];; searcht 5 [`mcell_set`;`cc_cell`];; searcht 5 [`NULLSET`;`cc_cell`];; searcht 5 [`edgeX`;`cc_cell`];; searcht 5 [`x IN cc_cell V ul`];; bb 3;; S_LEAF_IN_WEDGE_GE ;; searcht 5 [`leaf_rank`;name "INJ"];; searcht 5 [`azim a b c c = &0`];; searcht 5 [`periodic`;`leaf_rank`];; searcht 5 [`MOD`;`SUC`];; searcht 5 [`periodic`;`f (i MOD n)`];; Oxl_def.periodic_mod;; searcht 15 [`((i MOD n) + j) MOD n`;];; searcht 5 [`(a*n + i) MOD n`];; Leaf_cell.cc_cell;; searcht 5 [`cc_cell V a = cc_cell V b`];; searcht 5 [`stem [a;b;c]`];; searcht 5 [`stem`;`{a,b}`];; print_proof();; update_database();; (* Feb 3, 2013 *) Leaf_cell.ZASUVOR;; Leaf_cell.STEM_OF_LEAF;; searcht 50 [`hl`;`sqrt`;`barV`];; (* want barV as a conclusion if hl < sqrt2 *) Marchal_cells_3.HL_LE_SQRT2_IMP_BARV_1;; Leaf_cell.leaf;; MCELL4_FULL_WEDGE;; searcht 5 [`mcell4`;name "FIRST"];; searcht 5 [`cc_uh`;`barV`];; searcht 2 [`cc_cell`;`edgeX`];; searcht 2 [`NULLSET`;`cc_cell`];; EQ_SYM_EQ;; searcht 5 [`mcell_set`;`cc_cell`];; searcht 5 [`stem ul = {a,b}`];; searcht 5 [`cc_cell`;`convex hull s`];; searcht 8 [`mcell i V ul = mcell j V ul'`];; searcht 5 [`barV`;`cc_uh`];; searcht 5 [`cc_ke`;`3`;`4`];; INTER_IDEMPOT;; searcht 5 [`NULLSET`;`affine hull s`];; searcht 5 [`convex hull s SUBSET convex hull t`];; searcht 5 [`convex hull (affine hull s)`];; searcht 5 [`convex hull s = s`];; searcht 5 [`affine s ==> convex s`];; searcht 5 [`s SUBSET P hull t`];; searcht 5 [`set_of_list`;`LENGTH`;`4`];; searcht 5 [`barV`;`cc_uh`];; searcht 5 [`&0 < sin x`];; searcht 15 [`azim (vec 0) b c d`];; searcht 5 [`azim (a + x)`];; searcht 5 [`&0 <= azim a b c d`];; searcht 5 [`azim a b c d = &0`;`leaf_rank`];; searcht 5 [`i MOD n = i`];; searcht 5 [`n MOD n`];; Oxl_def.periodic_mod;; searcht 5 [`cc_cell`;`convex hull s`];; searcht 15 [`convex hull s = convex hull s'`];; searcht 5 [`affine_dependent`;`aff_dim`];; bb 5;; searcht 5 [`affine hull (convex hull s)`];; searcht 5 [`aff_dim`;`affine hull s`];; searcht 5 [`set_of_list`;`cc_uh`];; searcht 15 [`CARD`;`4`;`{a,b}`];; Leaf_cell.LENGTH4_SET2;; searcht 15 [`CARD`;; MCELL4_CARD4;; searcht 5 [`aff_dim`;`coplanar`];; searcht 5 [`coplanar`;`NULLSET`];; searcht 5 [`coplanar`;`convex hull s`];; searcht 5 [`int_of_num x = int_of_num y`];; searcht 5 [`mcell4`;`set_of_list`];; searcht 5 [`CARD`;`aff_dim`];; AFF_DIM_LE_CARD;; searcht 5 [`CARD {a,b,c,d} <= 4`];; searcht 5 [`cc_ke`;`&0 < chi_msb V ul`];; searcht 5 [`chi_msb a b = -- chi_msb a' b'`];; CC_CELL_WEDGE_MATCH_UH;; searcht 5 [`MOD`;`periodic`;`f i = f j`];; searcht 5[`(x MOD n) MOD n`];; searcht 5 [name "INJ";`azim`];; searcht 5 [`azim a b c c = &0`];; searcht 5 [`i MOD n = j MOD n`];; searcht 5 [`~(i MOD n = j MOD n)`];; LEAF_RANK4_CHI_MSB_ALT;; searcht 5 [`mcell4`;`set_of_list`];; searcht 5 [`set_of_list ul = {EL 0 ul, EL 1 ul, EL 2 ul, EL 3 ul}`];; searcht 5[`barV`;`LENGTH x = k + 1`];; searcht 15 [`left_action_list`;`barV`];; searcht 15 [`cc_cell V a = cc_cell V b`];; LEAF_RANK4_CHI_MSB_ALT;; searcht 5 [`CARD`;`4`;`cc_uh`];; searcht 5 [`barV`;`cc_uh`];; searcht 5 [`NULLSET`;`cc_cell`];; CC_CELL_WEDGE_MATCH_UH_ALT;; LEAF_RANK_AZIM_INJ;; Oxl_2012.MOD_INJ1;; searcht 5 [name "WEDGE_UNIQUE"];; searcht 5 [`i MOD n MOD n`];; searcht 8 [`(a + b) MOD n`];; searcht 5 [`i MOD n = i`];; print_proof();; update_database();; (* Feb 5, 2013 *) WEDGE_UNIQUE_CC_CELL;; searcht 5 [`cc_ke`;`3`;`4`];; searcht 5 [`barV`;`cc_uh`];; searcht 1 [`edgeX`;`cc_cell`];; Leaf_cell.cc_cell;; searcht 5 [`SUC i + n - 1`;`MOD`];; searcht 5 [`cc_cell V a = cc_cell V b`];; searcht 5 [`e IN critical_edgeX V X`];; searcht 5[`sum {}`];; searcht 5 [`mcell4`;name "FIRST"];; searcht 5 [`NULLSET`;`edgeX`];; searcht 5 [`sum`;`edgeX`];; searcht 2 [`cc_cell`;`edgeX`];; print_proof();; update_database();; Print_types.print_goal_types();; (* Feb 6, 2013 *) cc_prep_model_data;; searcht 5 [`leaf_rank`;`cc_ke`];; searcht 5 [`leaf_rank`;`s_leaf`];; S_LEAF_SYM;; searcht 5 [`barV`;`cc_uh`];; searcht 5 [`gammaX`;`&0 <= x`];; Tskajxy.GAMMAX_GAMMA2_X;; searcht 5 [`gammaX`;`x >= &0`];; Tskajxy.TSKAJXY_1;; Tskajxy.TSKAJXY_2;; searcht 5 [`mcell`;`edgeX V X = {}`];; Bump.EDGE_IMP_K2;; searcht 5 [`&0 <= sum X f`];; searcht 5 [`FINITE`;`mcell_set`];; searcht 5 [`mcell_set`;`4`];; searcht 5 [`NULLSET`;`edgeX`];; searcht 5 [`critical_edgeX`;`hl`];; searcht 5 [`gammaX`;name "034"];; searcht 5 [`gammaX`;`mcell 3`];; searcht 15 [`gamma3f`];; searcht 5 [`eta_y`;`radV`];; searcht 5 [`eta_y a b c = eta_y a' b' c'`];; searcht 5 [`radV`;`hl`];; bb 3;; searcht 5 [`truncate_simplex 2 ul`];; searcht 5 [`collinear`;`ups_x`];; searcht 5 [`ups_x (x pow 2)`;`a * b * c`];; searcht 5 [`hl x <= hl y`];; searc 'a' 0 [`radV x <= radV y`];; searcht 5 [`aff_dim`;`affine_dependent`];; searcht 5 [`collinear`;`coplanar`];; searcht 5 [`coplanar (convex hull s)`];; searcht 5 [`convex hull s`;`mcell3`];; searcht 3 [`coplanar`;`NULLSET`];; searcht 5 [`affine_dependent`;`collinear`];; searcht 5 [`radV {x,y}`;`dist`];; searcht 5 [`barV`;`set_of_list ul SUBSET V`];; searcht 5 [`set_of_list ul = x INSERT y`];; searcht 5 [`collinear`;`~(x = y)`];; searcht 5 [`initial_sublist`;`CONS`];; searcht 15 [`truncate_simplex 2 ul`];; Marchal_cells.TRUNCATE_SIMPLEX_EXPLICIT_2;; Print_types.print_thm_types Marchal_cells.TRUNCATE_SIMPLEX_EXPLICIT_2;; searcht 5 [`CONS`;`[]`];; searcht 5 [`x = []`;`x = CONS u v`];; help_grep "CASE";; help "STRUCT_CASES_TAC";; searcht 5 [`initial_sublist []`];; searcht 5 [`initial_sublist`;`APPEND`];; searcht 5 [`aff_dim x = &0`];; searcht 5 [def "circum"];; searcht 5 [`circumcenter`;`voronoi_list`];; searcht 5 [name "XYOF"];; searcht 5 [`coplanar`;`affine_dependent`];; searcht 5 [`coplanar`;`aff_dim`];; searcht 5 [`aff_dim`;`coplanar`];; searcht 5 [`CARD`;`coplanar`];; searcht 5 [`CARD {a,b,c,d}`];; searcht 5 [`coplanar`;`coplanar_alt`];; searcht 5 [`voronoi_list V ul`;`voronoi_set`];; searcht 15 [`voronoi_set`];; Sphere.VORONOI_SET;; searcht 5 [`voronoi_set`;`circumcenter`];; searcht 50 [`circumcenter`];; searcht 5 [name "OAPV"];; searcht 5 [`affine hull s `;`coplanar`;`(:real^3)`];; searcht 5 [`coplanar`;`azim`;`pi`];; searcht 5 [`leaf_rank`;`azim`;name "INJ"];; searcht 5 [`SUC i MOD n`];; searcht 5 [`barV`;`x SUBSET V`];; searcht 5 [`truncate_simplex 2 (CONS x y)`];; searcht 5 [`mcell4`;`edgeX`];; searcht 5 [`vol`;`convex hull s`];; searcht 5 [`vol`;`NULLSET`];; searcht 5 [`collinear`;`~(a = b)`];; searcht 5 [`mcell4`;`convex hull s`];; searcht 5 [`wedge_ge`;`aff_ge`];; searcht 5 [`leaf`;`collinear`];; searcht 5 [`collinear`;`leaf_rank`];; searcht 5 [`convex hull s`;`aff_ge`];; MCELL3_DOMAIN;; searcht 5 [`truncate_simplex 2 ul = ul`];; searcht 5 [`leaf`;`collinear`];; searcht 5 [`delta_x`;`delta_y`];; searcht 5 [`sqrt8`;`sqrt2`];; searcht 15 [`rad2_x`];; searcht 5 [`dih_x a b c d e f < dih_x a' b' c' d' e' f'`];; Tame_inequalities.DIH_X_MONO_LT_4;; searcht 5 [`eta_x`;`rad2_x`];; searcht 5 [`x <= f(eta_x a b c)`;];; searcht 50 [`eta_y`;omit `ineq`];; Merge_ineq.rad2_x_eta_x;; Collect_geom.HVXIKHW;; SQRT_MUL;; searcht 5 [`sqrt x * sqrt x`];; searcht 5 [`x pow 2 <= y pow 2`];; searcht 5 [`max_real3`];; searcht 5 [`x <= max_real u v`];; searcht 5 [`ups_x`;`collinear`];; Collect_geom.COL_EQ_UPS_0;; print_proof();; update_database();; Print_types.print_goal_types();; WEDGE3_Y4;; (* Feb 7, 2013 *) searcht 5 [`rad2_y`;`rad2_x`];; searcht 5 [`sqrt8 * sqrt8`];; searcht 15 [`ups_x (y * y) ( u * u) (v * v)`];; searcht 5 [`dih_y`;` pi`];; searcht 5 [`atn2 (x,y)`;`pi / &2`];; searcht 5 [`atn (x) < pi/ &2`];; searcht 5 [`atn2`;`atn`];; searcht 5 [`&0 < atn x`];; searcht 5 [`atn u < c`];; ATN_BOUNDS;; Flyspeck_constants.bounds;; searcht 5 [`hminus`;`DECIMAL`];; searcht 5 [`sqrt2`;`sqrt8`];; searcht 5 [`sqrt8 < y`];; bb 4;; searcht 5 [`azim`;`dihV`];; searcht 5 [`dih_y`;`dihV`];; searcht 5 [`delta_x (x *x )`;`delta_y`];; searcht 5 [`azim`;`delta_x`];; searcht 35 [def "^delta"];; (* no vector version *) print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Merge_ineq.GDRQXLGv2 ;; WEDGE3_Y4;; (* Feb 8, 2013 *) searcht 5 [`coplanar_alt`;`delta`];; Collect_geom2.POS_EQ_NOT_COPLANANR;; searcht 5 [`coplanar`;`coplanar_alt`];; searcht 5 [`delta`;`delta_x`];; searcht 5 [`delta_x (x *x)`;`delta_y`];; searcht 5 [`azim a b c c `];; searcht 5 [`barV`;`set_of_list ul SUBSET V`];; searcht 5 [`azim`;`dihV`];; searcht 5 [`dihV`;`dih_y`];; searcht 5 [`rad2_x`;`radV`];; Merge_ineq.GDRQXLGv2;; searcht 5 [name "GDRQ"];; searcht 5 [`coplanar`;`CARD`];; type_of `coplanar`;; searcht 5 [`CARD {a,b,c,d}`];; searcht 5 [`rad2_y`;`rad2_x`];; searcht 5 [`&0 <= radV s`];; Rogers.AFFINE_HULL_RADV;; RAD_PI_IMP_WEDGE4;; searcht 5 [`sqrt2 * sqrt2`];; searcht 5 [`x * x <= y * y`];; searcht 15 [`abs x = x`];; searcht 5 [`gg_mcell`];; searcht 5 [`azim_mcell`];; searcht 5 [`cell_cluster_estimate_v1`;`edgeX`];; searcht 5 [`?`;`~collinear {a,b,c}`];; searcht 5 [`edgeX`;`~(u = v)`];; searcht 5 [`{a,b} = {c,d}`];; searcht 5 [`~a ==> ~b`];; searcht 5 [`FINITE`;`s_leaf`];; searcht 5 [`gg_mcell`;`gammaX`];; searcht 5 [`leaf_rank`;`periodic`];; searcht 5 [`sum`;`azim_mcell`];; searcht 5 [`hplus`;`sqrt2`];; searcht 5 [`azim_mcell`;`azim`];; searcht 5 [`bool_model_data_v10`;`cc_data_v4`];; searcht 5 [`hl [a;b]`];; cc_bool_model_data;; searcht 5 [`cc_data_v4`;`leaf_rank`];; searcht 5 [`cc_card_v10`;`cc_data_v4`];; searcht 5 [`cc_hassmall_v10`;`cc_data_v4`];; Oxl_def.cc_qx_v10;; type_of `(\x. azim_mcell V x u0 u1)`;; searcht 5 [`0..r`;`{i | i < j}`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Merge_ineq.GDRQXLGv2 ;; (* Feb 9, 2013 *) searcht 5 [`gamma4fgcy`;`gammaX`];; (* gamma4fgcy <=> gammaX *) Tskajxy_lemmas.gammaX_gamm4fgcy;; Merge_ineq.DIHV_DIH_X;; (* dihV <=> dih_x *) Merge_ineq.UPS_X_POS;; cell3_008_from_ineq;; Merge_ineq.ox3q1h_merge;; searcht 5 [`gg_mcell`;`gammaX`];; searcht 25 [`beta_bump_v1`];; searcht 5 [`beta_bump_force_y`];; Sphere.beta_bump_force_y;; Sphere.beta_bump_y;; searcht 5 [`cc_cell`;`wedge_ge`];; searcht 5 [`cc_ke`;`3`;`4`];; searcht 5 [`j < (n:num)`;`f (i:num) = f j`;`f (SUC i) = f (SUC j)`];; Bump.RIJRIED;; searcht 5 [`mcell_set`;`cc_cell`];; searcht 5 [`edgeX`;`cc_cell`];; searcht 15 [`mcell i V ul = mcell j V ul'`];; searcht 5 [`barV`;`cc_uh`];; searcht 5 [`mcell`;`cc_uh`;`cc_cell`];; Bump.RIJRIED;; searcht 8 [`EL`;`cc_uh`];; searcht 5 [`NULLSET`;`cc_cell`];; DIV_LE;; searcht 5 [`truncate_simplex (SUC n) (CONS x y)`];; searcht 5 [`set_of_list`;`CONS`];; searcht 5 [`truncate_simplex 0`];; searcht 5 [`inv (&0)`];; searcht 5 [`&0 <= x pow 2`];; searcht 5 [`truncate_simplex 0`];; searcht 15 [`truncate_simplex`;`initial_sublist`];; searcht 15 [`initial_sublist (CONS x y) (CONS x' y')`];; searcht 5 [`LENGTH (CONS x y)`];; searcht 5 [`initial_sublist []`];; searcht 5 [`LENGTH (truncate_simplex k ul)`];; searcht 5 [`initial_sublist(truncate_simplex k z) y`];; searcht 5 [`leaf`;`barV`];; searcht 5 [`x ==> (?u. p u)`];; searcht 5 [`(?x. P x) ==> q`;`!`];; searcht 5 [`P u ==> (?x. P x)`];; searcht 5 [`(?x. P x) ==> (?x. Q x)`];; searcht 25 [`p ==> (?x. Q x)`];; searcht 5 [`x <= (x:num)`];; searcht 5 [`DROP`];; searcht 5 [`truncate_simplex`];; searcht 50 [`APPEND`];; searcht 50 [`BUTLAST`];; searcht 5 [`initial_sublist a b /\ initial_sublist b c`];; searcht 5 [`1 <= LENGTH v`;`CONS`];; searcht 5 [`initial_sublist`;`BUTLAST`];; searcht 15 [`initial_sublist`];; searcht 5 [`APPEND a b = APPEND a' b'`];; searcht 5 [`initial_sublist x []`];; searcht 5 [`APPEND x y = []`];; searcht 5 [`LENGTH x = 0`];; searcht 5 [`?x y. u = CONS x y`];; searcht 5 [`CONS x y = []`];; searcht 5 [`SUC x = SUC y`];; searcht 5 [`initial_sublist`;`LENGTH`];; searcht 5 [`APPEND`;`LENGTH`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Merge_ineq.GDRQXLGv2 ;; (* Feb 11, 2013 *) searcht 5 [`CONS x (CONS y z)`;`LENGTH`];; searcht 5 [name "LENGTH_CONS"];; LENGTH0;; searcht 5 [`beta_bump_v1`;`sum`];; searcht 5 [`beta_bump_force_y`];; searcht 15 [`cc_4`];; searcht 5 [`leaf_rank`;`leaf`];; cc_4_cc_cell;; Oxl_merge.MCELL4_GG;; searcht 15 [`cc_uh`;`EL`];; searcht 15 [`beta_bump_v1`];; searcht 5[`mcell_set`;`cc_cell`];; searcht 5 [`NULLSET`;`cc_cell`];; searcht 5 [`barV`;`leaf`];; searcht 5 [`barV V 3`;`NULLSET`];; searcht 5 [`barV V 3`;`[u0;u1;f i;f (SUC i)]`];; searcht 5 [`barV`;`cc_uh`];; searcht 5 [`radV {a,b}`];; searcht 15 [`critical_edgeX`];; searcht 5 [`subcritical_edgeX`];; searcht 15 [`edgeX`;`mcell4`];; searcht 15 [`!x. (p ==> Q x)`;`(p ==> (!x. Q x)) <=> r`];; RIGHT_FORALL_IMP_THM;; searcht 5 [`edgeX`];; searcht 5 [`CARD e = 2`;`INSERT`];; searcht 5 [`edgeX`;`CARD`];; searcht 5 [`CARD {a,b,c,d}= 4`;`mcell4`;`4`];; searcht 5 [`CARD`;`~(a = b)`;`4`];; searcht 5 [`{a,b} = {c,d}`];; searcht 5 [`gammaX`;`gamma4fgcy`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Merge_ineq.GDRQXLGv2 ;; (* Feb 12, 2013 *) searcht 15 [`critical_weight`];; searcht 5 [`wtcount6_y`;`critical_weight`];; searcht 5 [`inv x = inv y`];; searcht 5 [`&x = &y`];; searcht 5 [`critical_edgeX`;`FINITE`];; searcht 5 [`CARD( x INSERT y)`];; searcht 5 [`CARD (Z INTER ((x INSERT y)))`];; CARD_CLAUSES;; searcht 5 [`(x INSERT y) INTER Z`];; searcht 5 [`FINITE (A INTER B)`];; MCELL4_EDGE_EXPLICIT;; searcht 5 [`{} INTER X`];; searcht 5 [`wtcount3_y`];; Pack_defs.critical_edgeX;; searcht 5 [`critical_edgeX`;`critical_edge_y`];; searcht 5 [`hl [a;b]`];; searcht 5[`{} INTER x`];; searcht 5 [`azim_mcell`;`azim`];; searcht 5 [`azim a b c d < pi`;`mcell4`];; searcht 15 [`azim`;`dihV`];; searcht 5 [`leaf`;`collinear`];; searcht 5 [`dihV`;`dih_y`];; EDGE_LE_2RAD;; searcht 5 [`radV`;`rad2_x`];; Collect_geom2.NOT_COPLANAR_IMP_CARD4;; searcht 5 [`coplanar (convex hull s)`];; searcht 5 [`mcell4`;`convex hull s`];; searcht 5 [`delta_y`;`coplanar`];; searcht 5 [`&0 < ups_x (dist(x,y) pow 2) b c`];; searcht 5 [`collinear`;`coplanar`];; searcht 5 [`barV`;`set_of_list ul SUBSET V`];; searcht 5 [`rad2_x a b c d e f = rad2_f a' b' c' d' e' f'`];; searcht 5 [`&0 <= radV s`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Collect_geom2.NOT_COPLANAR_IMP_CARD4;; (* Feb 13, 2013 *) searcht 5 [`x <= radV s`];; searcht 5 [`affine_dependent`;`coplanar`];; searcht 5 [`CARD`;`coplanar`];; searcht 8 [`CARD {a,b,c,d}`;`4`];; searcht 5 [`radV {a,b}`];; searcht 15 [`d pow 2 <= r pow 2`];; searcht 5 [`rad2_x`;`radV`];; searcht 5 [`{a,b} SUBSET {a',b',c,d}`];; searcht 5 [`CARD`;`~(a=b)`;`4`];; searcht 5 [`sqrt2 * sqrt2`];; searcht 5 [`x pow 2 <= r pow 2`];; searcht 5 [`&0 <= dist (x,y)`];; searcht 5 [`sqrt8 = &2 * x`];; searcht 5 [`cc_eps`];; searcht 5 [`gg_mcell`];; searcht 5 [`gammaX`;`gamma4fgcy`];; searcht 5 [`cc_4`;`beta_bump_v1 V e x = &0`];; searcht 5 [`hminus`;`sqrt8`];; searcht 5 [`radV`;`eta_y`];; searcht 5 [`d3`;`&0 <= eta_y a b c`];; searcht 5 [`dist`;`d3`];; searcht 5 [`collinear`;`leaf`];; searcht 5 [`gamma4fgcy a b c d e f r = gamma4fgcy a' b' c' d' e' f' r`];; searcht 5 [`rad2_y a b c d e f = rad2_y a' b' c' d' e' f'`];; searcht 5 [`azim_mcell`;`azim`];; WEDGE3_Y4;; searcht 5 [`azim_mcell`;`azim`];; searcht 5 [`leaf_rank`;`leaf`];; searcht 5 [`leaf V ul = leaf V ul'`];; searcht 5 [`s_leaf V ul = s_leaf V ul'`];; searcht 5 [`s_leaf`;`leaf`];; searcht 5 [`leaf_rank`;`s_leaf`];; LEAF_RANK_TRUNCATE;; searcht 5 [`leaf`;`s_leaf`];; searcht 5 [`NULLSET`;`cc_cell`];; searcht 5 [`collinear`;`leaf`];; searcht 5 [`eta_y a b c = eta_y a' b' c'`];; searcht 5 [`azim_mcell`;`sum`;`pi`];; searcht 5 [`hl [u;v]`];; searcht 5 [`hplus`;`sqrt2`];; searcht 3 [`sum`;`periodic`];; searcht 3 [`beta_bump_v1`;`bump`];; searcht 5 [`periodic`;`gg_mcell`];; searcht 15 [`sum (a..b)`;`SUC`];; SUM_CLAUSES_NUMSEG;; searcht 5 [`sum (a..a)`];; searcht 5 [`periodic`;`f i = f j`];; searcht 5 [`azim_mcell`;`sum`;`pi`];; searcht 5 [`cc_4`;`azim_mcell`;`dih_y`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Collect_geom2.NOT_COPLANAR_IMP_CARD4;; (* Feb 14, 2013 *) searcht 5 [`gammaX`;`gamma3f`];; searcht 5 [`mxi`;`sqrt2`];; searcht 5 [`barV`;`cc_uh`];; searcht 5 [`cc_uh`;`EL`];; searcht 5 [`gamma3f a b c r f =gamma3f a' b' c' r f`];; searcht 5 [`dih_y a b c d e f = dih_y a' b' c' d' e' f'`];; searcht 5 [`dihX V X (u0,u1) = dihX V X (u0',u1')`];; searcht 5 [`mcell_set`;`cc_cell`];; searcht 5 [`edgeX`;`cc_cell`];; searcht 5 [`gg_mcell`;`gamma4fgcy`];; searcht 5 [`gamma4fgcy a b c d e f r = gamma4fgcy a c b d f e r`];; searcht 5 [`gamma4fgcy a b c d e f r = gamma4fgcy a' b' c' d' e' f' r`];; searcht 5 [`rad2_y a b c d e f = rad2_y a' b' c' d' e' f'`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Collect_geom2.NOT_COPLANAR_IMP_CARD4;; (* Feb 15, 2013 *) searcht 5 [def "beta_bumpA_y"];; searcht 5 [`beta_bumpA_y`];; searcht 5 [`cc_4`;`azim_mcell`];; Merge_ineq.gamma_qx;; Merge_ineq.gamma10_gamma11;; searcht 5 [`hminus`;`DECIMAL`];; searcht 5 [`hplus`;`sqrt`];; searcht 5 [`wtcount6_y a b c d e f = wtcount6_y a' b' c' d' e' f'`];; Merge_ineq.cell3_from_ineq_thm;; searcht 3 [`radV`;`eta_y`];; searcht 5 [`collinear`;`leaf`];; searcht 7 [`x pow 2 < y pow 2`];; searcht 5 [`&0 <= sqrt2`];; searcht 5 [`&0 <= eta_y a b c`];; searcht 5 [`sqrt2 * sqrt2`];; searcht 5 [` gamma4fgcy a b c d e f r > &0`;omit `ineq`];; searcht 5 [`beta_bumpA_y a b c d e f = &0`];; searcht 5 [`norm2hh`;omit `ineq`];; searcht 15 [`hminus`;`sqrt8`;omit `ineq`];; searcht 5 [`beta_bumpA_y`;`beta_bump_lb`];; Merge_ineq.beta_bumpA_lb1 ;; searcht 15 [`#0.008`];; NO_4CELL_IMP_K3;; searcht 5 [`sum`;`gg_mcell`];; gg_mcell;; (*def*) searcht 5 [`sum`;`azim_mcell`];; searcht 5 [`sum (x INSERT y)`];; searcht 5 [`sum `;`DISJOINT`];; searcht 5 [`cc_cell`;`edgeX`];; searcht 5 [`mcell_set`;`cc_cell`];; searcht 5 [`FINITE`;`mcell_set`;`edgeX`];; searcht 5 [`sum{a,b}`];; Merge_ineq.cell3_008_from_ineq_ALT;; searcht 15 [`mcell3`;`gammaX`];; searcht 15 [`edgeX`;`mcell`];; searcht 5 [`mcell_set`;`mcell`];; searcht 5 [`mcell`;name "FIRST"];; Bump.LENGTH4;; Pack_defs.critical_weight;; searcht 5 [`critical_edgeX`;`edgeX`];; searcht 5 [`CARD x = 1`];; searcht 5 [`SING`];; searcht 8 [`edgeX`;`?`];; searcht 5 [`edgeX`;`mcell3`];; searcht 5 [`edgeX`;`mcell4`;`{a,b,c,d}`];; searcht 5 [`mcell3`;`CARD`];; searcht 5 [`truncate_simplex 2 [a;b;c;d]`];; searcht 5 [`cc_uh V ul = CONS x y`];; searcht 5 [`{a,b}= {c,d} ==> dist u = dist v`];; searcht 5[`leaf`;`barV`;`cc_uh`];; searcht 5 [`beta_bump_v1`;`mcell`];; Bump.MCELL_BUMP_0;; searcht 5 [`sum A f <= sum A g`];; searcht 5 [`edgeX`;`NULLSET`];; searcht 5 [`mcell2`;`#0.008`];; searcht 50 [`gamma2_x_div_azim_v2`];; Tskajxy.GAMMAX_GAMMA2_X;; searcht 5 [`dihX`;`mcell2`];; Tskajxy.MCELL2_DIHX;; searcht 5 [`mcell2`;name "FIRST"];; searcht 5 [`a * x < b * x`];; searcht 5 [`gamma2_x_div_azim_v2`;`gamma2_x_div_a_v2`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Collect_geom2.NOT_COPLANAR_IMP_CARD4;; (* Feb 17, 2013 *) searcht 5 [`hminus`;`<`];; Tskajxy.GAMMAX_GAMMA2_X;; searcht 5 [`dihV`;`dih_y`];; searcht 5 [`collinear`;`mxi`];; searcht 5 [`coplanar`;`mcell2`];; searcht 5 [`coplanar`;`collinear`];; critical_weight_wtcount6_y;; searcht 5 [`inv(x) = y`];; searcht 5 [`CARD x = 1`];; searcht 5 [`x IN critical_edgeX V X`];; searcht 5 [`edgeX`;`mcell2`];; searcht 5 [`gammaX`;`gamma3f`];; searcht 5 [`critical_weight`;`cc_cell`];; critical_weight_wtcount6_y;; critical_edgeX_critical_edge_y;; searcht 5 [`critical_edgeX`;`edgeX`];; searcht 5 [`CARD ((x INSERT y) INTER b)`];; searcht 5 [`FINITE`;`critical_edgeX`];; searcht 5 [`{} INTER B`];; searcht 5 [`critical_edgeX`;`edgeX`];; searcht 5 [`CARD`;`4`;`mcell3`];; searcht 5 [`CARD s = 4`;`~(a = b)`];; searcht 5 [`gamma3f a b c r f = gamma3f a' b' c' r f`];; searcht 5 [`eta_y a b c = eta_y a' b' c'`];; searcht 5 [`&0 <= sum s f`];; searcht 5 [`&0 <= dihX V x e`];; searcht 5 [`critical_weight`;`cc_cell`];; searcht 5 [`&0 <= critical_weight V X`];; searcht 15 [`&0`;`gammaX V X f`];; searcht 15 [`beta_bump_v1`;`cc_cell`];; searcht 5 [`sum s f = sum s g`];; searcht 5 [`beta_bump_v1 V e X = &0`];; searcht 5 [`a * sum s f`];; real_model_008;; searcht 5 [`mcell3`;name "FIRST"];; Bump.MCELL_BUMP_0;; searcht 5 [`cc_cell`;`edgeX`];; searcht 5 [`dihX V X e = dihX V X e'`];; searcht 5 [`mcell_set`;`cc_cell`];; searcht 5 [`azim_mcell`;`azim`];; Sphere.b_spine5;; searcht 5 [`gamma23_keep135_x`;name "Merge_ineq"];; TSKAJXY_3;; searcht 5 [`gammaX`;`gamma3f`];; searcht 5 [`gamma23_keep135_x`;`gamma3f`];; searcht 5 [`gamma23_keep135_x`;omit `ineq`];; searcht 5 [`gamma3_x`;`gamma3f`];; Merge_ineq.gamma3_x_gamma3f;; searcht 5 [`dih_y`;`dih_x`];; searcht 5 [`hl`;`eta_y`];; Collect_geom.POW2_COND_LT;; searcht 5 [`&0 <= eta_y a b c`];; searcht 5 [`sqrt2 * sqrt2`];; bb 4;; Nonlinear_lemma.dih_y_sym;; searcht 5 [`dihX`;`cc_cell`;`dih_y`];; mcell3_dihX_dih_y;; searcht 5 [`gamma23_full8_x`;`gamma3f`];; searcht 15 [`delta_x4`;`dih_x`];; searcht 5 [`&0 < atn2 (x,y)`];; searcht 5 [`&0 < atn x`];; searcht 8 [`&0 < x / y`];; searcht 5 [`hminus`;`DECIMAL`];; searcht 5[`abs (atn x)`];; searcht 5 [`tan(atn x)`];; searcht 5 [`sqrt s pow 2 = s`];; searcht 6 [`x pow 2 < y pow 2`];; searcht 5 [`x pow 2`;`eta_y`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Collect_geom2.NOT_COPLANAR_IMP_CARD4;; (* Feb 18, 2013 *) critical_weight1;; searcht 5 [`azim a b c d`;`dih_y`];; searcht 10 [`azim`;`dihV`];; searcht 5 [`dih_y`;`dihV`];; searcht 5 [`&2 <= dist(f i,f (SUC i))`];; searcht 5 [`radV`;`azim a b c d < pi`];; searcht 5 [`radV`;`rad2_x`];; searcht 15 [`coplanar`;`azim`];; searcht 5 [`coplanar`;`f i`;`f (SUC i)`];; searcht 15 [`azim a b c d = &0`];; searcht 5 [`leaf`;`cc_A0`];; searcht 3 [`aff_gt a s = aff_gt a t`];; searcht 5 [`aff_gt`;`aff_ge {a,b} {c}`];; searcht 5 [`collinear`;`DISJOINT`];; searcht 5 [`aff`;`collinear`];; searcht 5 [`dist(x,x)`];; searcht 5 [`delta_y`;`coplanar`];; GSYM (REWRITE_RULE[LET_DEF;LET_END_DEF] GDRQXLGv3);; searcht 5 [`&2`;`sqrt2 * sqrt2`];; searcht 10 [`x pow 2 <= y pow 2`];; searcht 5 [`eta_y`;`x pow 2 <= y pow 2`];; searcht 5 [name "TRUNCATE_SIMPLEX_EXPLICIT"];; searcht 5 [name "Local_lemmas1"];; searcht 5 [name "Local_lemmas"];; searcht 5 [name "MOD_REFL"];; MOD_REFL;; searcht 5 [name "EJR"];; REBIND_TAC;; searcht 5 [`x IN {(a,b) | f a b}`];; searcht 15 [`!(x:A#B). f x`;`!a b. g a b`];; FORALL_PAIR_THM;; IN_ELIM_PAIR_THM;; searcht 5 [`(a,b) = (c,d)`];; searcht 5 [`?v. P v /\ (p = v)`];; searcht 50 [`fan`];; searcht 50 [`base_point_fan`];; searcht 15 [`FAN`;`SUBSET`];; searcht 5 [`dart1_of_fan`;`dart_of_fan`];; type_of `nn_of_hyp`;; searcht 5 [`azim_cycle`;`sigma_fan`];; searcht 5 [`azim_cycle`];; searcht 5 [`ivs_azim_cycle`;`inverse_sigma_fan`];; searcht 50 [`dih2k`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Collect_geom2.NOT_COPLANAR_IMP_CARD4;; (* Feb 21, 2013 *) searcht 5 [`gamma2_x1_div_a`];; searcht 5 [`gamma2_x1_div_a`];; searcht 5 [`beta`];; searcht 5 [`radius`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.ALL_TO_THE_NONPARALLEL_PART;; (* Feb 22, 2013 *) searcht 5 [`azim_cycle`];; searcht 5 [`sigma_fan`];; searcht 15 [`inverse1_sigma_fan`;`inverse_sigma_fan`];; searcht 15 [`ivs_azim_cycle`];; searcht 25 [`dart1_of_fan`];; searcht 5 [name "PAIR";name "ELIM"];; searcht 5 [`{a,b} = {b,a}`];; searcht 5 [`ivs_azim_cycle {}`];; searcht 5 [`wedge_ge`];; searcht 15 [`hypermap`];; type_of `face_set`;; searcht 5 [`face`;`face_set`];; searcht 5 [name "WRGC"];; type_of `hro`;; dest_const `hro`;; type_of `rho`;; searcht 5 [def "rho_node"];; type_of `rho_node1`;; searcht 50 [`rho_node1`;`FST`];; searcht 5 [`rho_node1`];; searcht 5 [name "KOMW"];; searcht 15 [`rho_node`];; searcht 5 [`rho_node1`;`rho_node`];; searcht 5 [`per`];; searcht 5 [`perimeterbound`];; searcht 5 [`tauVEF`];; searcht 50 [`w_node_fan`];; searcht 50 [`wedge_in_fan_ge`];; searcht 50 [name "LVD"];; searcht 5 [name "RNS"];; searcht 5 [def "fan80"];; searcht 5 [`fan80`;`convex_local_fan`];; searcht 5 [name "CIZM"];; searcht 25 [def "flat"];; searcht 5 [name "LDU"];; searcht 5 [def "straight"];; searcht 5 [name "HKIR"];; searcht 5 [name "interior_angle1"];; searcht 50 [`interior_angle1`];; searcht 5 [name "KOM"];; searcht 5 [name "OZQ"];; searcht 5 [name "KCH"];; searcht 5 [name "HKIR"];; searcht 5 [name "EGH"];; searcht 5 [name "deform"];; searcht 5 [name "XRECQNS"];; searcht 5 [`deformation`];; searcht 5 [def "^FAN$"];; searcht 5 [`FAN`;`fan1`];; searcht 5 [`slicef`;`f_slice`];; searcht 15 [def "slice"];; searcht 5 [`slice`];; searcht 50 [`f_slice`];; List.length (searcht 50 [`e_slice`]);; searcht 50 [`slicef`];; searcht 50 [name "Wjs"];; searcht 100 [name "Dih2k_";omit `vecmat`;omit `dimindex`];; searcht 5 [name "COMPATIBLE_BW_TWO_LEMMAS2"];; searcht 5 [name "EJRC"];; searcht 5 [`sol_local_fan`];; searcht 5 [`azim_in_fan`;`interior_angle1`];; searcht 5 [`v_prime`];; searcht 5 [`v_prime`];; searcht 8 [`aff_gt {x} {y}`];; searcht 5 [`v IN wedge a v c d`];; searcht 5 [`collinear {a,b}`];; searcht 7 [`v,rho_node1 FF v`];; searcht 5 [`convex_local_fan`;`local_fan`];; searcht 5 [`{v,v} = {v}`];; searcht 5 [`CARD`;`EE`];; searcht 1 [`v IN v_prime V U`];; searcht 5 [`face HS a INTER face HS b`];; searcht 5 [`mdtau_y_LC`];; searcht 1 [`safesqrt`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.ALL_TO_THE_NONPARALLEL_PART;; (* Feb 23, 2013 *) searcht 50 [name "Arc_properties"];; searcht 50 [name "Ckqowsa."];; searcht 50 [`tame_13a`];; type_of `deformation`;; type_of `localization`;; type_of `taum`;; searcht 5 [def "stable"];; searcht 5 [`lunar_deform`];; searcht 5 [`spherical_map`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types SUM_CONST;; (* Feb 24, 2013 *) searcht 5 [`slicev`;`CARD`];; searcht 15 [`v_prime`;`CARD`];; Local_lemmas1.CONDS_IN_V_PRIME_NUM2;; Local_lemmas1.CONDS_IN_V_PRIME_NUM;; searcht 5 [`rho_node1`;`v_prime`];; Local_lemmas1.POINTS_IN_HAFL_CIRCLE;; searcht 5 [`ITER i (rho_node1 FF) v IN V`];; Local_lemmas.LOCAL_FAN_ORBIT_MAP_VITER;; searcht 5 [`ITER n f v = v`;`rho_node1`];; Local_lemmas1.CARD_IS_LEAST_CYCLE;; Local_lemmas.LOFA_IMP_ITER_RHO_NODE_ID;; searcht 5 [`POWER`;`ITER`];; searcht 5 [`ITER`;`?`;`rho_node1`;`v IN V`];; searcht 5 [`coplanar`;`plane`];; searcht 50 [`plane`];; searcht 5 [`local_fan`;`CARD`;`EE`];; searcht 5 [`aff_gt`;`wedge`];; searcht 5 [`wedge`;`wedge_ge`];; searcht 5 [`wedge_in_fan_gt`;`{}`];; searcht 5 [`wedge a b c d = {}`];; searcht 5 [`collinear`;`rho_node1`];; searcht 5 [`collinear`;`azim_cycle`];; searcht 5 [`collinear`;`ivs_rho_node1`];; searcht 5 [`azim_cycle`;`ivs_rho_node1`];; searcht 5 [`x IN wedge a b c d `];; searcht 5 [`azim a b c c`];; searcht 5 [`ITER (a + b)`];; searcht 5 [`slicev`;`v_prime`];; searcht 5 [`local_fan`;`convex_local_fan`];; searcht 15 [`CARD`;`local_fan`];; Local_lemmas.ITER_CARD_MINUS1_EQ_IVS_RN1;; searcht 5 [`ITER 0`];; searcht 5 [`{a,b}={b,a}`];; searcht 5 [`(w,rho_node1 FF w) IN FF`];; searcht 5 [`rho_node1 FF (ivs_rho_node1 FF v)`];; REWRITE_RULE[TAUT `(a ==> b ==> c) <=> (a /\ b ==> c)`] Local_lemmas1.CONDS_IN_V_PRIME_NUM;; searcht 5 [`A SUBSET B /\ B SUBSET A`];; searcht 5 [`v_prime`;`ITER`];; searcht 5 [`v_prime V f SUBSET E`];; help_grep "GEN";; help "X_GEN_TAC";; searcht 5 [`ITER i (rho_node1 FF) v = ITER j (rho_node1 FF) v`];; Local_lemmas1.LT_CARD_MONO_LOFA;; searcht 5 [`IMAGE`;`CARD`];; searcht 5 [`FINITE`;`{i | (i:num) < j}`];; searcht 5[ `CARD`;`{i | (i:num) < j}`];; searcht 5 [`{a,b,c} = {a,c,b}`];; searcht 50 [`generic`];; searcht 5 [`e_prime`;`SUBSET`];; searcht 5 [`aff_ge {a} {b,c}`;`aff_gt`];; searcht 5 [`(A UNION B) INTER C`];; searcht 5 [`A SUBSET {}`];; searcht 5 [`A UNION B SUBSET C`];; searcht 5 [`aff_ge`;`aff_lt`;`collinear`];; searcht 5 [`aff_ge {a} {b}`;`aff_lt`];; searcht 5 [def "aff_ge"];; searcht 5 [`aff_ge`;`affsign`];; searcht 5 [`aff_ge {a} {b}`;`%`];; searcht 5 [`aff_lt {a} {b}`;`%`];; searcht 5 [`a % (vec 0)`];; searcht 5 [`a % y = vec 0`];; searcht 5 [`v_prime V fw SUBSET V`];; searcht 5 [`wedge_in_fan_gt`;`wedge`];; searcht 5 [`vec 0 + a`];; searcht 5 [`collinear`;`%`];; searcht 5 [`interior_angle1`;`azim_in_fan`];; searcht 5 [`convex_local_fan`;`slicev`];; Local_lemmas1.CONDS_IN_V_PRIME_NUM2;; Polar_fan.LOCAL_FAN_ORBIT_MAP_EXPLICIT;; searcht 15 [`IMAGE`;`?`];; searcht 5 [`SURJ`;`IMAGE`];; searcht 5 [`CARD V = 0`];; searcht 5 [`FINITE`;`local_fan`];; searcht 5 [`BIJ`;`CARD`];; searcht 5 [`FINITE {i | i < (j:num)}`];; searcht 5 [`FINITE(A UNION B)`];; searcht 5 [`CARD`;`{x | f (x:num)}`;`(a:num) <= b`];; searcht 5 [`CARD (A UNION B)`];; searcht 5 [`ITER 0`];; searcht 5 [`CARD {}`];; searcht 5 [`CARD {a}`];; searcht 5 [`CARD (a..b)`];; searcht 5 [`a..b`;`(a:num) <= x`];; searcht 15 [`local_fan`;`CARD:(real^3#real^3->bool) -> num`];; searcht 25 [`local_fan`;`CARD:(real^3->bool) -> num`];; Local_lemmas1.LOFA_HYP_UNION_CARD_GT2;; searcht 15 [`ITER`;`rho_node1`];; Local_lemmas.LOFA_IMP_LT_CARD_SET_V;; searcht 5 [`BIJ`;`sum`];; searcht 5 [`BIJ`;`local_fan`];; searcht 5 [`sum V f = sum V g`];; searcht 5 [`interior_angle1`;`azim_in_fan`];; searcht 15 [`v,rho_node1 FF v`];; searcht 5 [`local_fan`;`FST x IN V`];; searcht 5[`local_fan`;`v_prime V fv,E,f`];; Local_lemmas1.HAFL_CIRCLE_FORM_LOCAL_FAN;; Local_lemmas1.HAFL_CIRCLE_FORM_LOCAL_FAN2;; searcht 5[`&a + &b`];; searcht 5 [`&a = &b`];; X_CHOOSE_TAC;; searcht 5 [`BIJ`;`CARD`];; searcht 5 [`FINITE`;`local_fan`];; bb 4;; Local_lemmas.LOFA_IMP_CARD_FF_V_EQ;; searcht 5 [`2 <= CARD x`];; searcht 5 [`FINITE`;`local_fan`];; searcht 5 [`sum V (\e. f e - c)`];; searcht 5 [`sum V (\e. f)`;`CARD`];; searcht 5 [`x:(A->B)->(C->D)->(A#C) -> (B#D)`];; searcht 15 [`x:(A->B->C)->(B->A->C)`];; searcht 10 [def "rho"];; searcht 5 [`sol_y`;`sol0`];; searcht 5 [`taum`;`rho_fun`];; searcht 5 [`rhazim`];; searcht 5 [`const1`];; searcht 5 [`ly`;`lnfun`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types SUM_CONST;; (* Feb 26, 2013 *) searcht 5 [`tau_fun`];; searcht 5 [`main_estimate`];; searcht 5 [`#0.206`];; searcht 5 [`d_tame`];; searcht 5 [`diagonal1`];; searcht 5 [`protracted`];; searcht 5 [name "AZIM_SUM"];; searcht 5 [`arcV`;`rho_node`];; searcht 20 [`azim a b c d + azim a b d e`];; searcht 5 [name "KCH"];; searcht 5 [`azim a b c d = pi`];; searcht 5 [def "power_map_points"];; searcht 5 [`power_map_points`];; searcht 5 [`sigma_fan`;`rho_node1`];; searcht 5 [def "if_azims_fan"];; searcht 23 [`azim_cycle`];; searcht 5 [`azim_cycle`;`cyclic_set`];; TOPOLOGICAL_SORT;; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types SUM_CONST;; (* March 2, 2013 *) searcht 5 [`(a:num) * i + b`;`MOD`];; searcht 5 [`k - (a MOD k)`];; searcht 5 [`MOD`;`(a:num) - b`];; searcht 5 [`FST (SND (SND(SND x)))`];; searcht 10 [def "^part"];; type_of `taustar`;; searcht 5 [`{i | F}`];; searcht 5 [`part0`];; (* March 18, 2013 *) help "MK_CONJ";; searcht 5 [`periodic {}`];; searcht 50 [def "min"];; searcht 5 [`min_num`];; type_of `MEM`;; searcht 5 [`sol_local`];; searcht 5 [`circular`];; searcht 5 [`azim_in_fan`];; type_of `min_num`;; type_of `max_num`;; searcht 5 [`max_num`];; type_of `max`;; type_of `scs_J_v4 s`;; (* March 31, 2013 *) searcht 5 [def "assoc"];; searcht 5 [`ASSOC`];; searcht 5 [`MAP`];; (* April 1, 2013 *) help_grep "list";; listof;; mk_list;; help "mk_flist";; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types SUM_CONST;; (* April 17, 2013 *) searcht 15 [`taum`];; searcht 0 [`&0 <= sol_x y1 y2 y3 y4 y5 y6`];; searcht 0 [`sol_x`;`&0`];; searcht 0 [`&0`;`sol_euler_x_div_sqrtdelta`];; searcht 0 [`sol_x`;`x:real^3`];; searcht 5 [`sol`;`dihV`];; searcht 2 [`&0 <= sol a b`];; Counting_spheres.SOL_NN;; searcht 5 [`sol`;`dihV`];; Tskajxy_lemmas.SOL_SOLID_TRIANGLE;; searcht 5 [`dihV`;`dih_y`];; Merge_ineq.DIHV_EQ_DIH_Y;; searcht 5 [`dih_y`;`sol_y`];; Sphere.sol_y;; searcht 5 [`sol_x`;`sol_y`];; searcht 5 [`collinear`;`ups_x`];; searcht 5 [`ups_x a b c = ups_x a' b' c'`];; searcht 5 [`radial`;`convex hull S`];; MEASURABLE_RULES;; searcht 5 [`primitive`];; searcht 5 [`solid_triangle`];; searcht 5 [`convex hull S`;` normball`];; searcht 5 [name "NKEZ"];; searcht 5 [`sol_local`];; Nkezbfc_local.SOL_LOCAL_FAN_POS_CASE3;; searcht 15 [`convex_local_fan`];; searcht 5 [`local_fan`;`convex_local_fan`;`FAN`];; searcht 5 [def "sol_eu"];; searcht 5 [`sol_euler_x`;`delta_x`];; searcht 15 [`eulerA_x`;omit `compose6`];; searcht 5 [`cstab`;`DECIMAL`];; Merge_ineq.sol_x_sol_euler_x;; searcht 5 [`eulerA_x`;`sqrt`];; Sphere.eulerA_x;; searcht 5 [`sqrt(x *y) = sqrt x * sqrt y`];; searcht 5 [`&0 < atn2 (x,y)`];; Euler_main_theorem.EULER_TRIANGLE;; searcht 5 [`dihV`;`coplanar`];; DIHV_EQ_0_PI_EQ_COPLANAR;; searcht 5 [`dih_x a b c d e f = pi`];; searcht 15 [`azim a b c d = pi`];; searcht 5 [`atn2`;`dih_x`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types SUM_CONST;; (* April 17, 2013 *) searcht 5 [`cstab`;`DECIMAL`];; searcht 5 [`sol0`;`DECIMAL`];; searcht 5 [`taum`;`rhazim`];; searcht 5 [`&0 <= dih_x y1 y2 y3 y4 y5 y6`];; searcht 5 [`dih_y`;`rhazim`];; searcht 5 [`a <= rho y`];; searcht 5 [`ly y`;`<=`];; searcht 5 [`rho`;`lfun`];; searcht 5 [`rho y = x`];; searcht 5 [`const1`;`DECIMAL`];; searcht 5 [`const1`;`sol0`];; searcht 5 [`atn2(&0,x)`];; searcht 5 [`delta_y y1 y2 y3 y4 y5 y6 = delta_y y'1 y'2 y'3 y'4 y'5 y'6`];; searcht 5 [`delta_x y1 y2 y3 y4 y5 y6 = delta_x y'1 y'2 y'3 y'4 y'5 y'6`];; searcht 5 [`delta_x4 y1 y2 y3 y4 y5 y6 = delta_x4 y'1 y'2 y'3 y'4 y'5 y'6`];; UNDISCH;; searcht 5 [`dih_x y1 y2 y3 y4 y5 y6`;`pi`];; searcht 5 [`sol_y`;`sol_x`];; searcht 5 [`ups_x (a*a) (b*b) (c*c) = u`];; searcht 5 [`tau_residual_x`];; searcht 15 [`taum_x`;`rhazim_x`];; searcht 5 [`taum`;`rhazim`];; searcht 5 [`sqrt(x * x)`];; searcht 5 [`scs_k_v14 s = y`];; searcht 5 [`{i | F}`];; searcht 5 [`sum {}`];; searcht 5 [`ball_annulus`;`h0`];; searcht 5 [`IMAGE v S SUBSET U`];; searcht 5 [`taum`;`rhazim`];; searcht 5 [`rhazim`;`rho`];; searcht 5 [`dihV`;`dih_y`];; searcht 5 [`collinear`;`ball_annulus`];; Dih2k_hypermap.NONPARALLEL_BALL_ANNULUS;; searcht 5 [`norm`;`dist`;`vec 0`];; searcht 5 [`norm(v-w)`;`dist`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types SUM_CONST;; (* April 19, 2013 *) searcht 5 [`&0`;`delta`;`dist`];; searcht 5 [`delta`;`delta_x`];; searcht 5 [`norm`;`dist`];; searcht 5 [`MAP f []`];; searcht 5 [`i MOD k = i`];; searcht 5 [`d_tame2`];; Sphere.tame_table_d;; help_grep "recurs";; help "new_recursive_definition";; searcht 5 [`(a,b) = (c,d)`];; type_of `ASSOCD_v18`;; searcht 5 [`taum y1 y2 y3 y4 y5 y6 = taum y'1 y'2 y'3 y'4 y'5 y'6`];; searcht 5 [`taum`;`rhazim`];; searcht 5 [`&2 <= sqrt8`];; 0.103 +. 2.0 *. 0.2759;; NONPARALLEL_BALL_ANNULUS_ALT;; searcht 5 [`tau_star`];; searcht 5 [`tauVEF`;`tau_fun`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types SUM_CONST;; (* April 21, 2013 *) searcht 5 [name "EJRCF"];; searcht 2 [`tauVEF`];; searcht 5 [`tau_fun`;`sum`];; searcht 5 [`azim_dart`;`azim_in_fan`];; searcht 5 [def "azim_dart"];; searcht 5 [`azim_dart`;`azim_fan`];; searcht 5 [`azim_in_fan`;`azim_fan`];; searcht 5 [`azim_fan`];; searcht 5 [`periodic {}`];; searcht 5 [`a * k + b:num`;`MOD`];; searcht 5 [`periodic`;`MOD`];; searcht 5 [`i MOD k < k`];; searcht 5 [`(a ==> b) /\ (b ==> a)`];; searcht 15 [`(!x. (a ==> b x)) <=> (a ==> (!x. b x))`];; [GSYM (REWRITE_RULE[Appendix.periodic2] periodic2_funlist);GSYM (REWRITE_RULE[Appendix.periodic2] periodic2_funlistA)];; searcht 15 [`sum (A INTER B)`;`FINITE`];; searcht 5 [`sum`;`SUBSET`;`&0`];; searcht 5 [`sum A f = sum A g`];; SUM_CLAUSES;; searcht 5 [`FINITE`;`INSERT`];; searcht 5 [`tau_fun`];; searcht 5 [`tau_fun`;`tauVEF`];; searcht 15 [`tauVEF`];; searcht 5 [`&(x - y) `];; searcht 5 [`rho_fun`;`lmfun`];; searcht 5 [`azim_dart`;`azim_in_fan`];; searcht 5 [`rho_fun`;`rho`];; searcht 5 [`rho`;`lfun`];; searcht 5 [`rho_fun`];; searcht 5 [`rho`];; searcht 5 [`const1`;`sol0`];; searcht 5 [`ly`;`lmfun`];; searcht 5 [`azim_dart`;`azim_fan`];; searcht 0 [`azim_in_fan`;`azim_fan`];; searcht 0 [`azim_in_fan`;`azim_dart`];; Tame_general.ly_EQ_lmfun;; searcht 5 [`ly`;`lfun`];; searcht 5 [def "azim_in_fan"];; searcht 5 [`azim_cycle`;`sigma_fan`];; searcht 5 [`azim_cycle`;`azim_in_fan`];; searcht 5 [`azim`;`azim_fan`];; searcht 5 [def "EE"];; searcht 5 [def "set_of_edge"];; searcht 5 [`set_of_edge`;`EE`];; searcht 5 [`FAN`;`CARD`;`2`];; searcht 15 [def "FAN"];; searcht 5 [`FAN`;`fan2`];; searcht 5 [`graph`];; searcht 5 [`HAS_SIZE`;`{x}`];; searcht 5 [`FAN`;`local_fan`];; searcht 5 [`local_fan`;`{x,y} IN E`];; searcht 5 [`(i + k) MOD k`];; searcht 5 [`(a * k + b) MOD k`];; searcht 5 [`k MOD k`];; searcht 5 [`0 MOD k`];; searcht 5 [`CARD x <= CARD y`];; searcht 5 [`CARD {i | i <= k }`];; searcht 5 [`CARD (i..j)`];; searcht 5 [`(i..j)`;`{i | a <= i /\ i <= j}`];; IN_NUMSEG;; searcht 5 [`FINITE`;`{i | i < (j:num)}`];; Appendix.is_ear_v25;; searcht 5 [`unadorned_v25`];; searcht 5 [`i < j /\ j < 3`];; searcht 15 [`sqrt8`;`cstab`];; searcht 5 [`funlist_v25 a a0 k i i`];; searcht 5 [`k MOD k`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types SUM_CONST;; (* May 3, 2013 *) searcht 5 [`{i | F}`];; searcht 5 [`a INSERT b = {}`];; Appendix.get_main_nonlinear "5691615370";; searcht 5 [`IMAGE f X SUBSET Y`];; searcht 5 [`x IN ball_annulus`];; searcht 5 [`i MOD k = i`];; searcht 5 [`k MOD k`];; searcht 5 [`&0 <= delta_y a b c d e f`;`dist`];; bb 3;; Appendix.taustar_v25;; Merge_ineq.REAL_FINITE_MAX_EXISTS;; searcht 5 [name "WLOG";`P x1 x2 = P x2 x1`];; searcht 5 [`enclosed`];; searcht 5 [name "dart_leads_into_eq1"];; Appendix.tau_fun;; searcht 5 [`IMAGE`;`periodic`;`(:A)`];; searcht 5 [`CARD (IMAGE f X)`];; searcht 5[`FINITE`;`{i | (i:num) < j}`];; searcht 5 [`CARD`;`{i | (i:num) < j}`];; searcht 5 [`&(a - b)`];; searcht 5 [`sum (IMAGE f X) g`];; searcht 15 [`azim_in_fan`;`azim`];; searcht 5 [`azim_cycle`];; searcht 5 [def "EE"];; searcht 5 [`EE`;`IN`];; help_grep "GEN";; searcht 5 [`x IN IMAGE f X`];; searcht 5 [`{a,b} = {c,d}`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types SUM_CONST;; (* May 4, 2013 *) searcht 5 [`periodic`;`vv (i:num) = ww (i:num)`];; searcht 5 [name "FORALL";name "IMP"];; DIVISION;; searcht 5 [`(i + j) MOD k`];; searcht 5 [`(a * k + v) MOD k`];; searcht 5 [`azim_cycle`;`{a,b}`];; searcht 5 [`CARD {a,b}`];; searcht 5 [`~(a MOD k = b MOD k)`];; searcht 5 [`dist(x,x)`];; searcht 5 [`i MOD k = i`];; searcht 5 [`azim a b c d = azim a b c e + azim a b e d`];; searcht 7 [`sum ( a INSERT b)`];; searcht 5 [`convex_local_fan`;`azim_in_fan`];; Local_lemmas.PRIOR_TO_LESS_THAN_PI_LEMMA;; searcht 5 [`azim_in_fan`];; Localization.azim_in_fan;; searcht 5 [`rho_node1`];; searcht 15 [`rho_node1`;name "Localization."];; searcht 5 [`periodic`;`MOD`];; searcht 5 [`(a + j) MOD k`];; searcht 5 [`collinear`;`ball_annulus`];; searcht 5 [`ball_annulus = x`];; searcht 5 [`x pow 2 <= y pow 2 `];; searcht 5 [`IMAGE f X SUBSET Y`];; searcht 5 [name "EGH"];; Local_lemmas.EGHNAVX;; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; (* May 5, 2013 *) help_grep "SPEC";; help "GEN";; searcht 5 [`ITER 0`];; searcht 5 [`ITER (SUC j)`];; searcht 5 [`periodic`;`IMAGE`];; searcht 5 [`CARD (IMAGE f X)`];; NONPARALLEL_BALL_ANNULUS40_ALT;; searcht 5 [def "generic"];; searcht 5 [`generic`];; searcht 5 [`local_fan`;`convex_local_fan`];; Appendix.cstab;; searcht 15 [name "Tame_lemmas";`reflection`;`dist`];; searcht 15 [name "enclosed";name "Tame_lemmas."];; searcht 15 [name "quadratic";name "Tame_lemmas."];; searcht 50 [name "Tame_lemmas."];; searcht 5 [`enclosed`];; Collect_geom2.CAYLEYR_5POINTS;; POW_2_SQRT ;; DIST_POS_LE;; searcht 5 [`muR`];; Mur.muR;; searcht 5 [`cayleyR`];; searcht 5 [`abc_of_quadratic`];; searcht 5 [`delta`;`delta_x`];; searcht 3 [`&0 <= delta_y a b c d e f`;`dist`];; DELTA_Y_POS_4POINTS;; searcht 50 [`chi_msb`];; Tame_lemmas.delta_y_pos;; searcht 5 [`vec 0`;`cross`];; searcht 5 [`dot`;`cross`;`&0`];; searcht 5 [`cross`;`ups_x`];; searcht 5 [`&0 < norm x`];; searcht 5 [`&0 < x pow 2`];; searcht 5 [`&0 <= norm x`];; searcht 5 [`&0 < x dot x`];; searcht 5 [`chi_msb`;`coplanar`];; searcht 15 [`chi_msb`;`cross`];; searcht 5 [`coplanar`;`delta_y`];; REWRITE_RULE[LET_DEF;LET_END_DEF] enclosed4_lemma;; searcht 5 [`ups_x`;`collinear`];; GSYM Collect_geom2.NOT_COL_EQ_UPS_X_POS;; searcht 5 [`collinear`;`ball_annulus`];; searcht 5 [`chi_msb`;`coplanar`];; searcht 15 [`coplanar`;`collinear`];; searcht 5 [`convex_local_fan`;`pi`];; Local_lemmas.IN_V_IMP_AZIM_LESS_PI;; searcht 5 [name "Terminal";`rho_node1`];; searcht 5 [`wedge_ge`;`aff_ge`];; searcht 5 [`wedge_ge`;`azim`];; bb 3;; vv_azim_le;; REWRITE_RULE[LET_THM] vv_azim_le;; searcht 15 [`vv i = vv j`;`periodic`;`MOD`];; Local_lemmas.WEDGE_GE_EQ_AFF_GE;; searcht 15 [`aff_ge {a,b} {c,d}`;`%`];; searcht 5 [`DISJOINT`;`collinear`];; searcht 5 [`DISJOINT {a,b} {c,d}`];; searcht 5 [`chi_msb`;`%`];; searcht 5 [`chi_msb [a;b;c] d = -- chi_msb [a;b;c'] d'`];; searcht 5 [`azim a b c d = pi`;`aff`;`INTER`];; searcht 5 [`conv0`;`%`];; searcht 5 [`chi_msb u d = &0`];; searcht 5 [`set_of_list [a;b;c]`];; searcht 15 [`aff {u,v}`];; searcht 5 [`affine (P hull s)`];; searcht 5 [`S SUBSET P hull S`];; searcht 5 [`chi_msb u (a + b)`];; searcht 5 [`a * b <= &0`];; searcht 15 [`a * x = a * y`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; (* May 7, 2013 *) searcht 5 [`azim`;`dihV`];; Local_lemmas.AZIM_LE_PI_EQ_DIHV;; type_of `part8`;; searcht 5 [`drop3`];; searcht 5 [`part5`];; type_of `h0`;; frees (mk_flist terminal_cs);; map frees terminal_cs;; searcht 5 [`(a * k + b) MOD k`];; searcht 50 [name "Zithlqn."];; searcht 50 [name "Xwitccn.";`scs_lo_v28`];; searcht 5 [`pi`;`convex_locaL_fan`];; searcht 5 [name "convex_local"];; searcht 5 [`azim`;`azim_in_fan`];; searcht 5 [`azim_cycle {a,b}`];; searcht 5 [`rho`;`rho_fun`];; Local_lemmas.AZIM_LE_PI_EQ_DIHV;; searcht 5 [`&0 <= azim a b c d`];; searcht 5 [`collinear`;`ball_annulus`];; searcht 5 [`IMAGE f X SUBSET B`;name "Terminal"];; periodic_vv_inj;; searcht 5 [`{a,b,c} = {a,c,b}`];; UNDISCH;; UNDISCH terminal_quad_lemma;; vv_quad_split012;; searcht 5 [`vv i = vv (i MOD k)`];; periodic2_mod_reduce;; bb 5;; Appendix.cs_adj;; searcht 5 [`SUC 3 = 4`];; searcht 5 [`x IN ball_annulus`];; searcht 5 [`taum a b c d e f = taum a' b' c' d' e' f'`];; Merge_ineq.tau_x_tau_residual_x;; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; (* May 7, 2013 *) searcht 5 [`sqrt8 * sqrt8`];; searcht 5 [`dist`;`enclosed`];; searcht 5 [`tauq`;`taum`];; Appendix.get_main_nonlinear "4680581274 delta top issue";; searcht 5 [`delta_x4 a b c d e f = delta_x4 a' b' c' d' e' f'`];; searcht 5 [def "cayleyR"];; searcht 10 [`cayleyR x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 = y`];; searcht 5 [`tau3`;`taum`];; searcht 5 [`tau3 a b c = tau3 a' b' c'`];; searcht 5 [`dihV a b c d = dihV a b c' d'`];; bb 5;; searcht 5 [`INSERT`;`SUBSET`];; I_THM;; searcht 5 [`sqrt8`;`DECIMAL`;`pi`];; searcht 5 [name "safe"];; searcht 5 [`sin(azim a b c d)`];; searcht 8 [`dihV`;`azim`];; searcht 15 [`azim a b c d + azim a b d e`;omit `cyclic_set`];; searcht 15 [`cyclic_set`];; open Hales_tactic;; searcht 5 [`sqrt(y * y)`];; searcht 5 [`safesqrt x = sqrt x`];; searcht 5 [`safesqrt x`];; searcht 5 [`sqrt x * sqrt x `];; Functional_equation.functional_edge_flat2_x;; Functional_equation.functional_euler_3flat_x;; Functional_equation.functional_euler_2flat_x;; Functional_equation.functional_euler_1flat_x;; searcht 5 [def "ups_"];; searcht 10 [`abc_of_quadratic`];; searcht 5 [`quadratic_root_plus`];; Sphere.flat_term_x;; searcht 100 [def "min"];; searcht 8 [`min_num`];; State_manager.neutralize_state();; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; (* May 21, 2013 *) searcht 5 [`(x + y) * (x - y)`];; searcht 5 [`sqrt x * sqrt x`];; searcht 5 [`sqrt x = &0`];; searcht 5 [`&0 <= sqrt x1`];; searcht 5 [`&0 < sqrt x1`];; searcht 5 [`a* b <= c * b`];; searcht 5[ `flat_term x <= &0`];; searcht 5 [`a <= sqrt y`];; searcht 15 [`a <= b / c`];; searcht 50 [`has_real_derivative`;name "MAX"];; REAL_DERIVATIVE_ZERO_MAXMIN;; searcht 50 [`has_real_derivative`;` f (y:real) <= f x`];; (* good stuff *) Counting_spheres.REAL_CONVEX_ON_SECOND_SECANT;; REAL_CONVEX_ON_SECOND_DERIVATIVE;; REAL_CONVEX_ON_SECANT_DERIVATIVE;; searcht 5 [`real_continuous`];; searcht 5 [def "real_continuous"];; searcht 5 [`real_continuous`;`real_open`];; searcht 50 [`real_continuous`;`abs`];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; (* May 22, 2013 *) searcht 5 [`has_real_derivative`;`delta_x`];; strip_comb `derived_form p f f' x s`;; Calc_derivative.derived_form_sin;; help_grep "strip";; strip_forall;; GEN_LIST;; help_grep "GEN";; GENL;; searcht 5 [`sqrt x = &0`];; searcht 5 [`derived_form F`];; Functional_equation.nonfunctional_taud_D1;; searcht 5 [`sqrt(x * x)`];; has_real_derivative;; searcht 5 [`(f has_real_derivative f') net ==> (g has_real_derivative f') net`];; snd(chop_list 50 (searcht 150 [`has_real_derivative`]));; drop;; Arc_properties.HAS_REAL_DERIVATIVE_LOCAL;; searcht 5 [`atreal`;`within`;`(:real)`];; WITHIN_UNIV;; searcht 5 [`real_open`;`>`];; derived_form_delta_y;; searcht 5 [`sqrt x = &0`];; searcht 5 [`taum`;`delta_y`];; open Terminal;; "2314572187";; searcht 5 [`taud`;`taud_x`];; Merge_ineq.tau_x_tau_residual_x;; searcht 5 [`tau_residual_x`;`taum_x`];; searcht 5 [`const`;`sol0`];; searcht 5 [`has_real_derivative`;`real_continuous`];; searcht 5 [`abs (&0)`];; searcht 5 [`real_open`;`<`];; searcht 5 [`real_interval`;`real_open`];; searcht 5 [`real_interval`];; searcht 5 [`real_interval (a,b)`];; searcht 5 [`z IN real_interval s`];; searcht 5 [`is_real_interval(real_interval (a,b))`];; searcht 5 [`real_interval(a,b) = {c}`];; searcht 5 [`(\x. -- f x)`;`has_real_derivative`];; searcht 5 [`atreal x within s`;`real_open`];; searcht 5 [`real_open(real_interval(a,b))`];; searcht 5 [`(\x. c) has_real_derivative u`];; searcht 5 [`has_real_derivative`;name "UNI"];; REAL_DERIVATIVE_UNIQUE_ATREAL;; searcht 15 [`real_open`;`real_continuous_on`];; searcht 15 [`real_closed`;`real_continuous_on`];; searcht 15 [`real_closed`;`x <= y`];; searcht 5 [def "compact"];; searcht 5 [`real_compact`;`real_closed`];; REAL_COMPACT_EQ_BOUNDED_CLOSED;; REAL_OPEN_DIFF;; REAL_CONTINUOUS_ATTAINS_INF;; searcht 15 [`real_open`;`PREIMAGE`];; searcht 50 [`open_in`;`real_continuous_on`];; searcht 5 [`real_continuous_on`;`real_compact`];; searcht 500 [`real_open`];; searcht 15 [`real_continuous`;`has_real_derivative`];; searcht 5 [`real_continuous_on`;`real_continuous`];; searcht 5 [`atreal x within (:real)`];; searcht 5 [`(\x. f x + g x) real_continuous z`];; searcht 5 [`(\x. c * f x) real_continuous z`];; searcht 15 [`(\x. g x * f x) real_continuous z`];; searcht 5 [`(\x. c) real_continuous z`];; searcht 5 [`(\x. (sqrt (f x))) real_continuous z`];; searcht 5 [`sqrt`;`real_continuous`];; searcht 5 [`(f o g) real_continuous z`];; searcht 5 [`real_continuous`;`SUBSET`];; searcht 5 [`real_continuous_on`;`SUBSET`];; searcht 5 [`real_bounded (X)`;`SUBSET`];; searcht 5 [`real_bounded (real_interval s)`];; searcht 5 [`real_closed`;`d <= t`];; searcht 5 [`real_open`;`d < t`];; searcht 5 [`min`];; searcht 5 [name "EXISTS";`?f. p ==> Q f`];; SPEC `t:real` (ASSUME `!(x:real). &3 > &4 * x`);; SPECL;; strip_forall;; help_grep "EXIST";; help "EXISTS";; help_grep "comb";; help_grep "exist";; searcht 5 [`x / y = &0`];; searcht 5 [`&0 <= x / y`];; searcht 5 [`&0 < x pow n`];; searcht 5 [name "taum_taum_x"];; print_proof();; update_database();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; (* May 24, 2013 *) searcht 15 [`mud_126_x_v1`];; searcht 5 [`delta_x y1 y2 y3 y4 y5 y6 = delta_x a b c d e f`];; searcht 5 [`taum y1 y2 y3 y4 y5 y6 = taum a b c d e f`];; searcht 5 [`taud`;`taum`];; searcht 5 [`flat_term`;`sol0`];; searcht 5 [`flat_term2_126_x`];; bb 3;; searcht 15 [`abc_of_quadratic`;`edge_flat2_x`];; searcht 50 [`abc_of_quadratic`];; searcht 15 [`quadratic_root_plus`];; searcht 5 [`a pow 2 < b pow 2`;`abs`];; searcht 5 [`flat_term`;`flat_term_x`];; searcht 5 [name "AFFSIGN_MONO_SHUFFLE"];; searcht 5 [`taud`;`flat_term_x`];; searcht 5 [`taud`;`taud_x`];; UNDISCH taud_minimizer_terminal_pent_cases;; UNDISCH OWZLKVY4;; help_grep "REP";; replicate;; REPEATC;; UNDISCH;; searcht 5 [`taum`;`taud`];; searcht 5 [`mud_126_x_v1`;`taud`];; (UNDISCH2 edge2_flatD_x1_delta_lemma3);; UNDISCH2 delta_126_x_2h0_le_d;; searcht 5 [`flat_term`;`taud`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; bb 3;; (* May 24, 2013 *) searcht 5 [`a <= sqrt b`];; searcht 25 [`a <= c /\ b <= d`;`a * b <= c * d`];; REAL_LE_MUL2;; delta_126_135;; searcht 5 [`&0 <= taud a b c d e f`];; hd(Ineq.getexact "1008824382");; hd(Ineq.getexact "8875146520");; Ineq.getexact "1586903463";; searcht 5 [`#0.705`];; searcht 5 [`tau3 v0 v1 v2 + tau3 v0' v1' v2'`];; searcht 5 [`taud`;`taum`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; bb 3;; (* May 27, 2013 *) searcht 5 [`taum`;`taud`];; appendix_get_main_nonlinear "6877738680";; searcht 5 [`taud_x`;`taud`];; searcht 50 [name "WLOG"];; REAL_WLOG_LE;; Merge_ineq.REAL_WLOG_SIMPLEX_3d;; searcht 5 [`delta_234_x`];; searcht 5 [`mud_126_x_v1`];; searcht 10 [`flat_term2_126_x`];; searcht 5 [`eulerA`];; searcht 5 [`ineq`;omit `CONS`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; bb 3;; (* May 28, 2013 *) searcht 5 [`x + y = y + x`;`(a + b) + c = a + b +c `];; 3860.0/. 60.0;; searcht 5 [`taum`;`taud`];; searcht 15 [`v ==> (a = sqrt b)`];; help_grep "CONJ";; basic_rewrites();; searcht 5 [name "BETA"];; searcht 25 [`eulerA_x`];; searcht 25 [def "euler"];; searcht 15 [`sol_euler_x`];; searcht 5 [`dihV`;`sol`];; searcht 5 [`eulerA_x`;`euler_p`];; searcht 5 [`sqrt(x pow 2)`];; searcht 5 [`&0 <= dist(x,y)`];; searcht 5 [`dist(v2,v3)`;`dot`];; searcht 15 [`(u + v) dot w`];; searcht 5 [`x dot y = y dot x`];; searcht 5 [`delta_x4`;`dihV`];; searcht 5 [name "EULER";`euler_p`];; searcht 5 [`dihV v0 v1 v2 v3 = &0`];; searcht 5 [`azim v0 v1 v2 v3 = pi`];; searcht 15 [`delta_x`;`v:real^3`];; searcht 5 [`&0 < atn2(d,p)`];; searcht 5[`&0 <= delta_y a b c d e f `;`dist`];; searcht 15 [`atn2`;`atn`];; Pent_hex.derived_form_delta_x;; searcht 5 [`dihV`;`delta_x4`];; searcht 5 [`atn2 (-- x, -- y)`];; searcht 5 [`atn x < pi / &2`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; bb 5;; (* May 31, 2013 *) searcht 5 [`coplanar`;`delta_y`];; searcht 5 [`eulerA_x a b c d e f = eulerA_x a' b' c' d' e' f'`];; searcht 15 [`delta_x`;`pow `;`delta_x4`];; searcht 5 [`delta_x`;`dih_x`];; searcht 5 [`ups_x`;`dot`];; derived_form_delta_x_wrt_x5;; searcht 5 [`delta_x a b c d e f = delta_x a b' c' d' e' f'`];; searcht 5 [name "Terminal";`main_nonlinear_terminal_v6`];; searcht 5 [`sqrt(&4)`];; searcht 5 [`sqrt(x) = &0`];; searcht 5 [`sqrt(x pow 2)`];; searcht 5 [`&0 < x pow 2`];; searcht 5[`atn2 (t * x, t * y)`];; searcht 5 [name "taustar_taum"];; open Terminal;; taustar_taum;; searcht 5 [name "AZIM_DIHV_SAME_STRONG"];; searcht 5 [name "Lunar_deform"];; searcht 5 [name "AZIM_EQ_IMP"];; searcht 5 [`convex_local_fan`];; List.length Build.build_sequence;; searcht 50 [def "_eq"];; searcht 50 [def "continuous"];; searcht 15 [`real_continuous`];; searcht 5 [def "generic"];; searcht 5 [`generic`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; Print_types.print_term_types AXJRPNC_concl;; bb 5;; (* Jun 17, 2013 *) searcht 5 [`lunar`];; searcht 55 [def "BB"];; searcht 5 [`arcV`;`dihV`];; searcht 5 [name "XWN"];; searcht 5 [def "d_fun3"];; searcht 5 [def "edge2_flatD_x1"];; searcht 5 [`edge2_flatD_x1`;`quadratic_root_plus`];; searcht 5 [name "IV"];; searcht 5 [`?x. f (x:real) = &0 /\ P x`];; searcht 15 [`real_continuous_on`;`f x = a`];; Sphere.abc_of_quadratic;; searcht 5 [`abc_of_quadratic (\z. f z)`];; searcht 50 [`derived_form`;`?`];; searcht 15 [`real_continuous`;`has_real_derivative`];; HAS_REAL_DERIVATIVE_IMP_CONTINUOUS_ATREAL;; searcht 5 [`real_continuous_on`;`real_continuous`];; searcht 5 [`x within (:real)`];; REAL_IVT_INCREASING;; searcht 5 [`edge2_flatD_x1 d x2 x3 x4 x5 x6 = x1`];; searcht 5 [`f real_continuous x within s`;`f real_continuous atreal x`];; searcht 5 [`delta_x`;`edge2_flatD_x1`];; searcht 5 [`quadratic_root_plus`;name "work"];; searcht 5 [`ups_x x1 x2 x3 = ups_x a b c`];; searcht 5 [`delta_x a b c d e f = delta_x a b' c' d' e' f'`];; searcht 5 [`delta_x1 a b c d e f = delta_x1 a b' c' d' e' f'`];; searcht 5 [`delta_y a b c d e f = delta_y a b' c' d' e' f'`];; searcht 5 [name "WLOG";name "SQ"];; Terminal.REAL_WLOG_SQUARE_LEMMA;; Pent_hex.delta_diff;; searcht 5 [`&0 < ups_x (a*a) (b*b) (c*c)`];; Merge_ineq.UPS_X_POS;; Pent_hex.delta_diff;; searcht 5 [`&0 <= abs(x)`];; searcht 5 [`abs(a / b)`];; searcht 5 [`a * x pow 2 + b * x + c`;`quadratic_root_plus`];; searcht 5 [`&0 <= x pow 2`];; searcht 5 [`sqrt(x pow 2 ) = abs x`];; searcht 5 [`x * x < y * y`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; Print_types.print_term_types AXJRPNC_concl;; bb 5;; (* Jun 19, 2013 *) searcht 5 [`x * x <= y * y`];; searcht 5 [`x pow 2 <= y pow 2`];; searcht 5 [`sqrt8 * sqrt8`];; searcht 5 [`&0 <= ups_x (a*a) (b*b) (c*c)`];; searcht 5 [`ups_x a b c = ups_x a' b' c'`];; searcht 50 [`delta_x`;`ups_x`];; searcht 5 [`xrr`];; searcht 5 [`derived_form F`];; searcht 5 [`derived_form b f f' x s = derived_form b' g g' x' s'`];; searcht 5 [`(f has_real_derivative f' x) s /\ (f has_real_derivative g' x') s'`];; searcht 5 [`f has_real_derivative f' x s`];; searcht 5 [def "has_real_derivative"];; searcht 5 [`has_real_derivative`;name "UNI"];; searcht 5 [`(atreal x within (:real))`];; searcht 5 [`re_eqvl`;`?`];; searcht 50 [`(f has_real_derivative (f x)) s`];; Vukhacky_tactics.HAS_REAL_DERIVATIVE_CHAIN2;; searcht 5 [`real_open`;`has_real_derivative`];; searcht 500 [`derived_form`];; Arc_properties.HAS_REAL_DERIVATIVE_LOCAL;; searcht 5 [`re_eqvl a b <=> re_eqvl b a`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; Print_types.print_term_types AXJRPNC_concl;; bb 5;; (* Jun 20, 2013 *) searcht 5 [`taum`;`rhofn`];; searcht 5 [`taum_x`];; searcht 5 [`taum`;`rhazim`];; searcht 5 [`dih_x a b c d e f = dih_x a' b' c' d' e' f'`];; searcht 50 [`real_open`];; searcht 5 [`real_open`;`<`];; searcht 5 [`real_continuous_on`;`!`;`?`];; Pent_hex.continuous_preimage_open;; searcht 5 [`real_continuous`;`has_real_derivative`];; HAS_REAL_DERIVATIVE_IMP_CONTINUOUS_ATREAL;; searcht 5 [`real_continuous`;`real_continuous_on`];; derived_form_xrr;; GEN_ALL Calc_derivative.derived_form_sub;; searcht 15[`ups_x (y1*y1) (y2*y2) (y6*y6)`];; searcht 15 [`&0 < x * y`];; searcht 15 [`x * y < &0`];; searcht 5 [`arclength`;`acs`];; searcht 5 [`sqrt x = &0`];; searcht 5 [`(f x - f y) = f' * (x - y)`;`has_real_derivative`];; searcht 15 [`&0 <= a * b`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; Print_types.print_term_types AXJRPNC_concl;; bb 3;; (* Jun 21, 2013 *) searcht 5 [`xrr y2 y3 y4 < &16`];; searcht 5 [` &0 < x pow 2`];; searcht 5 [`real_closed`;`real_interval`];; searcht 5 [`&0 < x/y`];; searcht 5 [`ups_x`;`xrr`];; searcht 5 [`&0 < x * y`;`\/`];; searcht 5 [`real_open`;`delta_y`];; searcht 5 [`taum`;`dih_x`];; searcht 5 [`x / y = &0`];; searcht 5 [`sqrt x = &0`];; searcht 5 [`&0 <= x / y`];; REAL_MVT_SIMPLE;; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; Print_types.print_term_types AXJRPNC_concl;; bb 3;; (* Jun 22, 2013 *) searcht 5 [`derived_form`;`(\q. g' (f q) * f' q)`];; searcht 5 [`&0 < x`;`delta_x`;`delta_y`;`xrr`];; derived_form_xrr;; searcht 5 [`real_open`;`real_interval`];; REAL_MVT_SIMPLE;; searcht 5 [`(atreal x within s)`;`f has_real_derivative f' atreal x`];; HAS_REAL_DERIVATIVE_ATREAL_WITHIN;; searcht 5 [`(f has_real_derivative f') (atreal x) ==> (f has_real_derivative f') (atreal x within s)`];; searcht 5 [`derived_form b (g o f)`];; GSYM Calc_derivative.derived_form;; derived_form_sum_dih444sub;; searcht 5 [`real_interval(a,b) SUBSET real_interval[a,b]`];; searcht 5 [`taum`;`dih_x`];; searcht 5 [`rho_fun y <= c`];; searcht 5 [def "rho"];; searcht 5 [`rho y = x`];; searcht 5 [`const1`;`sol0/pi`];; searcht 5 [`&0 < const1`];; searcht 5 [`xrr y1 y3 y5`;` &16`];; searcht 5 [`x * x < y * y`];; searcht 5 [`&0 < ups_x (a*a) (b*b) (c*c)`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types vv_azim_le;; Print_types.print_term_types t';; bb 3;; (* Jun 22, 2013 *) searcht 5 [`taustar_v39`;`mk_unadorned`];; searcht 5 [`scs_k_v39`;`mk_unadorned_v39`];; searcht 5 [`dsv_v39`;`mk_unadorned`];; Terminal.tau_fun_azim;; searcht 5 [`dist(x,x)`];; searcht 5 [`i MOD k = i`];; searcht 5 [`azim`;`tau_fun`];; searcht 5 [name "VPW";name "PRIME"];; searcht 5 [`SUC i MOD k`];; searcht 15 [`(i + a) MOD k`];; GSYM Oxl_2012.MOD_INJ1;; searcht 5 [`ball_annulus`;`norm`];; Fnjlbxs.in_ball_annulus;; searcht 5 [`IMAGE`;`SUBSET`];; searcht 5 [`dist(a,b)+dist(b,c)`];; searcht 5[`#2.52`;`h0`];; searcht 5 [`delta_y`;`norm`];; REWRITE_RULE[LET_THM] Tame_lemmas.delta_y_pos;; searcht 15 [name "JKQ"];; searcht 15 [`is_scs_v39`;`mk_unadorned_v39`];; searcht 50 [`mk_unadorned_v39`;`funlist_v39`];; Terminal.is_scs_funlist;; searcht 5 [`funlistA_v39`;`F`];; searcht 5 [`periodic {}`];; searcht 5 [`funlist_v39`;`cs_adj`];; Terminal.periodic2_funlist;; searcht 5 [`X SUBSET Y`;`CARD`];; searcht 5 [`{i | i < (k:num)}`];; searcht 5 [`CARD {}`];; searcht 5 [`x MOD k = SUC x MOD k`];; searcht 5 [`d_tame`;`#0.712`];; searcht 5 [`sol_local`;`azim_in_fan`];; searcht 5 [`generic`;`circular`;`lunar`];; searcht 5 [`convex_local_fan`;`local_fan`];; searcht 15 [`lunar`];; searcht 15 [`sol_local`];; searcht 15 [`interior_angle1`;`azim`];; searcht 5 [def "interior_an"];; searcht 5 [`interior_angle1`];; searcht 5 [`azim`;`rho_node1`;`ivs_rho_node1`];; searcht 5 [`rho_node1`;`i+1`];; SUM_SUB;; searcht 5 [`FINITE {i | i < (k:num)}`];; searcht 5 [`sum X (\x. c)`;`CARD`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; Print_types.print_term_types t';; bb 6;; (* Jun 24, 2013 *) Local_lemmas.CVX_LO_IMP_LO;; Wrgcvdr_cizmrrh.CIZMRRH;; searcht 5 [`interior_angle1`;`azim_in_fan`];; Wrgcvdr_cizmrrh.lunar;; searcht 5 [name "vv_rho_node1"];; Terminal.EE_vv;; Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; searcht 15 [`azim_in_fan`;`azim`];; DIVISION;; searcht 5 [name "SYN"];; searcht 10 [`dihV`;`azim`];; GSYM Polar_fan.AZIM_DIHV_SAME_STRONG;; searcht 5 [`collinear`;`BBs_v39`];; Appendix.BBs_v39;; searcht 5 [`periodic`;`f (i MOD k)`];; searcht 5 [`dih_x`;`delta_x4`];; searcht 5 [`dih_x a b c d e f < dih_x a' b' c' d' e' f'`];; searcht 5 [`interior_angle1`;`&0`];; searcht 5 [`(!i j. i < k /\ j < k /\ v i = v j ==> i = j)`];; searcht 5 [`azim_in_fan`;`interior_angle1`];; DIVISION;; searcht 5 [`a *(k:num) + b `;`MOD`];; searcht 5 [`&0 < atn2(x,y)`];; searcht 5 [`atn2(&0,x)`];; searcht 5 [`dih_y`;`dih_x`];; searcht 5 [`dihV`;`dih_y`];; searcht 5 [`periodic`;`MOD`];; searcht 5 [`dist`;`norm`];; searcht 5 [`delta_y`;`norm`];; searcht 5 [`i MOD k = SUC i MOD k`];; searcht 15 [`(i + a) MOD k`;`~ x`];; Oxl_2012.MOD_INJ1;; searcht 5 [name "dec";name "Lp_d"];; searcht 5 [`delta_x4 a b c d e f = delta_x4 a' b' c' d' e' f'`];; Wrgcvdr_cizmrrh.CIZMRRH;; searcht 5 [`scs_generic`];; Local_lemmas.INTERIOR_ANGLE1_POS;; GSYM INTERIOR_ANGLE1_AZIM;; (REWRITE_RULE[LET_THM] (GSYM INTERIOR_ANGLE1_AZIM));; scs_6T1;; searcht 5 [`scs_basic_v39`];; searcht 5 [`mk_unadorned_v39`;`unadorned_v39`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; Print_types.print_term_types t';; bb 11;; (* Jun 25, 2013 *) searcht 5 [`cs_adj`;`scs_diag`];; searcht 5 [`SUC i MOD k`];; is_scs_6T1;; searcht 5 [`periodic`];; Pent_hex.terminal_pent_taum;; searcht 5 [`eulerA_x`;`dihV`];; searcht 5 [`azim_in_fan`;`convex_local_fan`];; azim_in_fan_azim;; searcht 5 [`generic`;`collinear`];; Nkezbfc_local.PROPERTIES_GENERIC_LOCAL_FAN;; searcht 5 [`sol`;`dihV`];; searcht 5 [`taum`;`sol0`];; searcht 5 [`taum`;`dih_x`];; Sphere.taum;; searcht 5 [`taum y1 y2 y3 y4 y5 y6 = x`];; Sphere.rhazim;; searcht 5 [`&0 <= sol_y y1 y2 y3 y4 y5 y6`];; Sphere.sol_y;; searcht 5 [`generic`;`azim`;`+`];; DIH_IMP_EULER_A_POS;; searcht 5 [`sol_euler_x_div_sqrtdelta`];; searcht 5 [`&0 < sol x y`];; searcht 5 [`taum`;`sol_y`];; searcht 5 [`sol`;`vol`];; searcht 5 [`convex hull x`;`measurable`];; searcht 5 [`radial_norm`;`convex hull x`];; searcht 5 [`&0 <= dih_y y1 y2 y3 y4 y5 y6`];; searcht 5 [def "sol_euler_x"];; searcht 5 [`sol_euler_x`];; Localization.convex_local_fan;; azim_in_fan_azim;; searcht 5 [`sol_local`;`azim`];; Terminal.vv_split_azim_generic;; searcht 5 [`sum (a INSERT b)`];; searcht 5 [`FINITE {}`];; searcht 5 [`FINITE {a,b,c}`];; searcht 5 [`&0 <= x`; `azim`];; searcht 15 [`azim`;`dihV`];; Polar_fan.AZIM_DIHV_SAME_STRONG;; searcht 5 [`collinear`;`generic`];; searcht 5 [`IN`;`IMAGE`;`UNIV`];; searcht 5 [`periodic`;`x+(b:num)`];; Appendix.tau3;; `(3 + 4) - 1`;; searcht 5 [`rho_fun`;`rho`];; Terminal.tau3_taum_40;; Pent_hex.terminal_pent_taum;; searcht 5 [`taum a b c d e f = taum a' b' c' d' e' f'`];; searcht 5 [`delta_y`;`norm`];; DIH_IMP_EULER_A_POS;; searcht 5 [`dist(x, vec 0)`;`norm`];; searcht 5 [`sol_x`;`dihV`];; searcht 5 [`dihV a b c d = dihV a b c' d'`];; searcht 5 [`dihV`;`dih_y`];; searcht 2 [`dih_y`;`sol_y`];; searcht 5 [`&0 <= sol_y a b c d e f`];; searcht 5 [name "VPW"];; searcht 5 [`norm (x - y) `;`dist`];; Sphere.packing;; searcht 5 [`packing`;`IN`];; IN_ELIM_THM;; searcht 15 [`(s INSERT b) c`];; searcht 5 [`periodic`;`MOD`];; searcht 5 [`periodic`;`sum`];; Oxl_def.periodic_sum;; searcht 5 [`sum`;`BIJ`];; searcht 5 [`sum X f = sum X g`];; help_grep "ARITH";; help_grep "NUM";; Local_lemmas.CVX_LO_IMP_LO;; DIVISION;; searcht 25 [`(j + i) MOD k`];; MOD_ADD_MOD;; searcht 5 [`i MOD k = i`];; searcht 15 [`(a + b) MOD k = (a'+ b') MOD k`];; Polar_fan.AZIM_DIHV_SAME_STRONG;; searcht 5 [`sqrt(x pow 2)`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; Print_types.print_term_types t';; bb 11;; (* Jun 26, 2013 *) searcht 5 [`delta4_squared_y`];; searcht 5 [`dih_y`;`dih_x`];; searcht 5 [`x pow 2 < y pow 2`];; searcht 5 [`&0 <= tan x`];; searcht 5 [`x * y < x' * y`];; searcht 15 [`a < x pow 2`];; searcht 5 [`tan`;`atn`];; searcht 5 [`atn x < atn y`];; searcht 5 [`dih_y a b c d e f = dih_y a' b' c' d' e' f'`];; searcht 5 [`delta_y a b c d e f = delta_y a' b' c' d' e' f'`;`&2`];; searcht 5 [`taum a b c d e f = taum a' b' c' d' e' f'`];; searcht 5 [`dih_x a b c d e f < dih_x a' b' c' d' e' f`];; Tame_inequalities.DIH_X_MONO_LT_4;; searcht 5 [`delta_y y1 y2 y3 y4 y5 y6 = &0`;`dih_y`];; Sphere.dih_x;; searcht 5 [`atn2(&0,x)`];; searcht 5 [`dih_x`;`pi`];; Oxlzlez.DIH_X_LT_PI;; searcht 15 [`delta_x`;`pow`];; searcht 5 [name "diff";`delta_x`];; searcht 5 [`delta_x`;`delta_x1`;`pow`];; searcht 5 [`dihV`;`dih_y`];; searcht 5 [`cs_diag`;`cs_adj`];; searcht 15 [`(a+B) MOD n`;omit `5`];; searcht 5 [`1 MOD 5`];; searcht 5 [`i < 4`;`\/`];; searcht 5 [name "funlist";name "expl"];; searcht 5 [`1 MOD 4`;`2 MOD 4`];; searcht 5 [`psort 4`];; searcht 5 [`CARD x <= 2`];; searcht 5 [`CARD x = 1`];; searcht 15 [`CARD`;`3`];; searcht 5 [`CARD X <= CARD Y`];; searcht 5 [`CARD`;`{i | (i:num) < k}`];; searcht 5 [`CARD s <= 2`];; searcht 5 [`CARD {a,b}`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; Print_types.print_term_types t';; bb 25;; (* Jun 27, 2013 *) searcht 2 [`delta_y`;`norm`];; get_main_nonlinear "5405130650";; searcht 5 [def "deform"];; searcht 5 [`deformation`];; searcht 15 [def "continuous"];; type_of `real_continuous_on`;; searcht 5 [`continuous_on`;`azim`];; searcht 5 [`real_continuous`;`dihV`];; searcht 5 [`continuous_on`;`dist`];; searcht 5 [`generic`];; searcht 15 [name "HYPERPL";name "SEP"];; SEPARATING_HYPERPLANE_CLOSED_POINT;; REAL_CONTINUOUS_AT_AZIM;; searcht 5 [`azim`;`real_continuous`];; searcht 5 [`real_continuous_on`;`real_uniformly_continuous_on`];; type_of `compact`;; searcht 15 [`compact`;`closed`];; searcht 15 [`compact`;`real_interval`];; searcht 5 [`real_continuous_on`;`dot`];; searcht 25 [`azim a b c d = pi`];; searcht 50 [`wedge_ge`;name "Cou"];; searcht 5 [def "wedge"];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; Print_types.print_term_types t';; let named s = searcht 50 [name s];; bb 25;; (* Jun 28, 2013 *) searcht 50 [`(A:(V)net)`;omit `atreal`;omit `at`];; searcht 50 [`mk_net`];; searcht 50 [`real_continuous`;`dist`];; Local_lemmas1.CON_ATREAL_REAL_CON2_REDO;; searcht 15 [`continuous`;name "COMPO"];; BILINEAR_CONTINUOUS_AT_COMPOSE;; searcht 15 [`continuous`;`h (f x) (g x) (g2 x)`];; Local_lemmas1.UPS_X_CONTS_FUNC;; Local_lemmas1.CONTINUOUS_PRESERVE_COLLINEAR;; searcht 5 [`continuous`;`collinear`];; searcht 5 [`delta_y`;`coplanar`];; searcht 50 [`real_continuous`;`<`;`?`];; searcht 5 [def "generic"];; searcht 50 [def "wedge"];; searcht 5 [`wedge`;`azim`];; searcht 5 [`aff_gt`;`wedge`];; searcht 5 [`wedge`;`DIFF`];; searcht 5 [`azim a b c d = &0`];; searcht 5 [`coplanar`;`cross`];; Local_lemmas1.AZIM_COND_FOR_COPLANAR;; Local_lemmas.NOT_COLL_IMP_COPL;; searcht 5 [`wedge_ge`;`aff_ge`];; searcht 15 [`collinear`;`cross`];; Local_lemmas.COLL_IFF_COLL_CROSS;; searcht 50 [`collinear`;`t % (u:real^A)`];; COLLINEAR_SPECIAL_SCALE;; searcht 5 [`azim`;`sin`;`pi`];; searcht 5 [`sin`;`azim`;`cross`];; Local_lemmas.SIN_AZIM_MUTUAL_SROSS;; searcht 5 [`sin`;`pi`;`&0 < sin x`];; searcht 5 [`azim a b c d <= pi`];; searcht 5 [`sin pi`];; searcht 5 [`&0 <= sin (azim a b c d)`];; searcht 5 [`(a cross b) dot c = (a' cross b') dot c'`];; searcht 5 [`&0 < x dot x`];; searcht 5 [`a cross b = vec 0`;`collinear`];; searcht 5 [`{a,b,c} = {a',b',c'}`];; searcht 5 [`-- (v cross w)`];; searcht 15 [`aff_ge {a} {c,d}`;`%`];; searcht 8 [`DISJOINT`;`collinear`];; searcht 5 [`v cross w = v`];; searcht 5 [`collinear {a,b}`];; searcht 5 [`aff_ge {a} {b,c}`;`%`];; searcht 5 [`coplanar{a,b,c}`];; searcht 5[`u IN aff_ge {u} {v,w}`];; searcht 5[`vec 0 IN aff_lt a b`];; searcht 50 [`aff_lt {a} {b}`];; searcht 15 [`coplanar`;`%`];; searcht 5 [`coplanar`;`cross`];; searcht 5 [`x dot (-- v)`];; searcht 5 [`x dot (u + v)`];; searcht 5 [`x dot (vec 0)`];; searcht 5 [`(v cross w) dot v`];; searcht 15 [`coplanar`;`%`;omit `~coplanar s`];; searcht 5 [`t % x IN wedge a b c d`];; searcht 5 [`wedge`;`azim`];; searcht 5 [`azim`;`%`];; searcht 5 [`aff_ge {a,b} {c,d}`;`%`];; searcht 5 [name "LDUR"];; searcht 50 [name "Lunar_de"];; searcht 5 [`azim a w v w`];; searcht 20 [`wedge_ge`;`SUBSET`];; searcht 20 [`wedge`;`afffine hull {a,c}`];; Local_lemmas.INTERIOR_ANGLE1_POS;; searcht 50 [name "Counting_";name "SPL"];; searcht 5 [`dihV`;`azim`];; searcht 5 [`azim`;`x < &2 * pi`];; searcht 5 [`sin`;`azim`;`cross`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; Print_types.print_term_types t';; bb 25;; (* Jun 28, 2013 *) searcht 15 [`aff_ge {a,b} {c}`;`%`];; searcht 5 [`DISJOINT`;`collinear`];; searcht 5 [`collinear`;`%`];; CROSS_EQ_SELF;; searcht 5 [`collinear`;`cross`];; searcht 5 [`v dot v = &0`];; searcht 5 [`collinear {a,b}`];; searcht 5 [`collinear {a,b,a}`];; searcht 5 [`cross`;`azim`];; searcht 5 [def "re_eqvl"];; searcht 5 [`re_eqvl`;`?`;`&0`];; searcht 5 [`re_eqvl a b <=> re_eqvl b a`];; Local_lemmas.SIN_AZIM_POS_PI_LT;; searcht 5 [`sin pi`];; searcht 5 [`&0 < sin x`];; searcht 5 [`&0 <= azim a b c d`];; CROSS_LMUL;; searcht 5 [`x cross x`];; searcht 5 [`&0 < x dot x`];; searcht 5 [`collinear`;`cross`];; searcht 5 [def "cycle"];; searcht 50 [`azim_cycle`;`azim`];; Wrgcvdr_cizmrrh.IDENTIFY_AZIM_CYCLE;; Wrgcvdr_cizmrrh.AZIM_CYCLE_PROPERTIES;; searcht 15 [`azim a b c d = azim a b c' d'`];; searcht 5 [`collinear`;`cross`];; searcht 5 [`DISJOINT`;`collinear`];; searcht 5 [`(a cross (b cross c))`;`dot`];; searcht 5 [`a cross b = -- (b cross a)`];; searcht 5 [`t % (u % v)`];; searcht 5 [`t % (a + b)`];; searcht 15 [`azim a b c d= &0`];; CROSS_EQ_SELF;; searcht 5 [`(a cross b) dot a`];; searcht 5 [`azim a b c c`];; EQ_SYM;; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; Print_types.print_term_types t';; bb 7;; (* Jun 30, 2013 *) searcht 5 [`aff_ge`;`aff_gt`];; searcht 5 [`FINITE`;`IMAGE`];; searcht 5 [`FINITE`;`{i | (i:num) <= m}`];; searcht 5 [`azim`;name "SHIFT"];; searcht 5 [`xrr`];; searcht 5 [`arclength a b c < arclength a' b' c'`];; searcht 5 [`u IN aff_ge {a,u} {c}`];; searcht 5 [`collinear`;`cross`];; Leaf_cell.AZIM_BASE_SHIFT_LE;; searcht 6 [`azim a b c d + azim a b d e`;omit `cyclic_set`];; searcht 5 [`&0 <= azim a b c d`];; searcht 5 [name "LDUR"];; searcht 5 [`plane`;`coplanar`];; Trigonometry2.coplanar1;; searcht 5 [name "GE_2_2"];; searcht 5 [name "EGH"];; searcht 5 [`affine hull s`;`aff_gt`];; searcht 5 [`aff_gt a b SUBSET aff_gt a' b'`];; searcht 5 [`x IN S ==> x IN g hull S`];; searcht 5 [`coplanar`;`affine hull s`];; searcht 5 [`coplanar`;`azim`];; searcht 5 [`conv0`;`conv`];; searcht 5 [`conv0 {a,b} SUBSET X`];; searcht 5 [`conv0`;`%`];; searcht 5 [`convex`;`aff_gt`];; searcht 5 [`aff {a,b}`;`%`];; searcht 10 [`collinear`;`%`];; searcht 5 [`a % u = a % v`];; searcht 5 [`a % b % c`];; Trigonometry2.AFF2_VEC0;;; searcht 5 [`&1 % v`];; searcht 5 [`aff_gt`;`conv0`];; searcht 5 [`aff_gt s t SUBSET aff_gt s' t'`];; searcht 5 [`wedge`;`aff_gt`];; searcht 15 [`collinear`;`cross`];; searcht 15 [`azim a b c d = &0`];; searcht 5 [`a IN aff_ge {b,a} s`];; searcht 5 [`wedge`;`azim`];; searcht 5[`azim`;`a % c`];; searcht 10 [`azim`;`&2 * pi`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; Print_types.print_term_types t';; bb 7;; (* July 1, 2013 *) searcht 5 [`circular`];; searcht 5 [def "deformation"];; searcht 5 [`deformation`;`real_interval`];; searcht 5 [`deformation`];; searcht 50 [`wedge_in_fan_gt`];; searcht 5 [name "AZIM_EQ_IMP"];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.AZIM_CYCLE_TWO_POINT_SET;; Print_types.print_term_types t';; bb 7;; (* July 3, 2013 *) searcht 5 [name "MHAE"];; searcht 5 [`lunar`;`convex_local_fan`;`IMAGE`;`interior_angle1`];; searcht 15 [`FINITE`;`FAN`];; searcht 100 [def "FAN"];; searcht 5 [`fan3`;`FAN`];; searcht 50 [`FAN u = y`;`graph`];; searcht 5 [`graph E`];; searcht 5 [`local_fan`;`FINITE`];; searcht 5 [`local_fan`;`convex_local_fan`];; searcht 5 [`wedge`;`azim`];; searcht 25 [`a < b /\ b < c`;`&2`];; searcht 5 [`real_open`;`real_interval`];; searcht 5 [name "xrr_pos"];; type_of `real_continuous_on`;; searcht 5 [`azim`;`&0`;`aff_ge`];; searcht 5 [`aff_ge`;`coplanar`;`wedge`];; searcht 5 [`open`;`wedge`];; searcht 30 [`azim a b c d = pi`];; searcht 15 [`aff_lt {a,b,c}`];; searcht 5 [name "LDU"];; searcht 5 [`coplanar`;`azim`;`&0`];; searcht 15 [`coplanar`;`collinear`];; searcht 15 [`affine hull {a,b,c}`;`%`];; Ckqowsa_4_points.in_affine_hull_lemma;; searcht 5 [`collinear`;`aff_dim`];; searcht 5 [def "DIM"];; searcht 5 [`aff_dim`;`INSERT`];; searcht 5 [`(a cross b) dot c = (a' cross b') dot c'`];; searcht 5 [`a cross a`];; searcht 5 [`&0 < a dot a`];; searcht 15 [`&0 <= x * y`];; searcht 5 [`cross`;`collinear`];; searcht 5 [`azim a b c d = pi`;`coplanar`;`&0`];; coplanar;; plane;; searcht 5 [`S SUBSET affine hull S`];; searcht 5 [`aff {a,b}`;`%`];; searcht 5 [`conv0`;`%`];; searcht 5 [`collinear {vec 0,a,b}`;`%`];; searcht 5 [`a % v = a % w`];; searcht 5 [`a % (b + c)`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types CONTINUOUS_AT_LIFT_DOT2;; Print_types.print_term_types t';; bb 8;; (* July 4, 2013 *) searcht 5 [`&0 <= azim a b c d`];; NONPLANAR_OPEN;; searcht 5 [`(\t. c) continuous atz`];; searcht 5 [`open`;`dot`;`>`];; searcht 5 [def "open"];; searcht 5 [`open`;`!`;`?`;`dist`];; searcht 15 [`dot`;`continuous`];; searcht 5 [`continuous`;`lift`;`real_continuous`];; searcht 5 [`lift`;`drop`;`continuous`];; searcht 5 [`continuous`;`cross`];; searcht 5 [`real_open`;`real_interval`];; searcht 5 [`real_open`;`{x | x > c}`];; searcht 5 [`continuous`;`(-- (v:real^A))`];; searcht 5 [`azim`;`real_continuous`];; searcht 5 [`azim a b c d = &0`;`aff_ge`];; searcht 5 [name "MIN";name "FINITE";omit `dimindex`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types CONTINUOUS_AT_LIFT_DOT2;; Print_types.print_term_types t';; bb 5;; let s = searcht 5;; RENAME_FREE_VAR (`f:real^3#real^3->real^3#real^3`,"Q") (* July 4, 2013 *) s [`local_fan`;`IMAGE`];; searcht 5 [name "XREC"];; s [`local_fan`;`convex_local_fan`];; rename;; s [`?(x:A#B). P x`];; SKOLEM_THM;; s [`local_fan`;`FINITE`];; searcht 5 [`local_fan`;`~(FF = {})`];; s [`IMAGE f X = {}`];; searcht 25 [`local_fan`;`(u,v)`];; searcht 5 [`x = p1,p2`];; searcht 8 [`?e. (p ==> q)`];; searcht 8 [`((?x. p) ==> q)`];; searcht 5 [`azim_in_fan`;`interior_angle1`];; Nkezbfc_local.CONVEX_LOFA_IMP_INANGLE_EQ_AZIM;; let named x = (searcht 3 [name x]);; searcht 5 [`azim_in_fan`;`azim`];; Local_lemmas1.AZIM_IN_FAN_RHOND_IVS_RHOND;; searcht 15 [`rho_node1`];; searcht 5 [`v,rho_node1 FF v IN FF`];; searcht 5 [`p1 IN (V:real^3->bool)`;`local_fan`;`(x:real^3#real^3) IN FF`];; searcht 10 [`rho_node1 FF v = w`];; searcht 5 [`azim`;`azim_in_fan`];; Local_lemmas1.AZIM_IN_FAN_RHOND_IVS_RHOND;; searcht 5 [`rho_node1 FF p1 IN V`];; searcht 5 [`~collinear s`;`local_fan`];; searcht 5 [`ivs_rho_node1 FF v = w`];; searcht 5 [`ivs_rho_node1 FF v,v IN FF`];; searcht 5 [`collinear`;`ivs_rho_node1`];; searcht 5 [`FST x,SND x`];; FST;; searcht 5 [`&0 < interior_angle1 v f p`];; searcht 25[`(x,y) IN U`];; searcht 5 [`FINITE`;`CROSS`];; searcht 5 [`local_fan`;`~(V = {})`];; searcht 5 [`V CROSS FF = {}`];; help_grep "BETA";; searcht 5 [`local_fan`;`{u,v} IN E`;`(u,v) IN FF`];; searcht 5 [`wedge_in_fan_ge`;`wedge_ge`];; searcht 15 [`local_fan`;`x = {u,v}`];; searcht 5 [`graph`;`FAN`];; s [`FAN`;`local_fan`];; searcht 5 [`graph `;`{u,v}`];; searcht 5 [`graph`;`HAS_SIZE`];; searcht 5 [`x HAS_SIZE 2`;`{a,b}`];; searcht 25 [`IMAGE`;`INSERT`];; searcht 5 [`{u,v} IN (E)`;`local_fan`;`(x:real^3#real^3) IN FF`];; searcht 5[`{a,b} = {c,d}`];; Local_lemmas.LOCAL_FAN_IMP_IN_V;; searcht 5 [`azim`;`azim_in_fan`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types CONTINUOUS_AT_LIFT_DOT2;; Print_types.print_term_types t';; bb 8;; (* July 7, 2013 *) searcht 5 [`{u,v} IN E`;`(u,v) IN FF`;`local_fan`];; searcht 5 [`convex_local_fan`;`local_fan`];; searcht 5 [`local_fan`;`collinear`];; searcht 5 [`v IN V`;`(u,v) IN FF`;`local_fan`];; searcht 5 [`~(u = vec 0)`;`local_fan`];; searcht 5 [`generic`;`collinear`];; searcht 5 [`collinear`;`wedge`];; searcht 5 [`collinear`;`cross`];; searcht 5 [`real_continuous`;`norm`];; searcht 5 [`norm`;`(x = vec 0)`];; searcht 5 [`real_continuous_on`;`real_continuous`];; searcht 15 [`f o g real_continuous net`];; searcht 5 [`(\t. c) continuous net`];; searcht 5 [`funlist`];; searcht 5 [`v cross w = v`];; searcht 5 [`collinear {a,b}`];; searcht 5 [`azim`;`wedge`];; searcht 5 [`azim a b c c `];; searcht 5 [`cross`;`continuous`];; searcht 5 [`(\t. f t) = f`];; searcht 5 [`continuous`;`(\(t:real). -- (f:real->real^A) t)`];; searcht 5 [`continuous`;`(--):real^A->real^A`];; searcht 5 [`x IN wedge_ge a b c d`];; searcht 5 [`wedge_ge`;`wedge_in_fan_ge`];; searcht 5 [`x IN wedge_ge a x b d`];; searcht 5 [`wedge_ge`;`azim`];; searcht 5 [`azim a b c b`];; NHCXLRV;; Oxl_2012.CHQSQEY;; Oxl_2012.MTMLSRF;; Oxl_2012.LXDEYBO;; Oxl_2012.UNPNFVW;; Oxl_2012.DHCVTVE;; Oxl_2012.PMZTATI;; Oxl_2012.IPVICGW;; searcht 5 [`ivs_rho_node1 FF w IN V`];; searcht 5[`collinear`;`rho_node1`];; searcht 5 [`collinear`;`local_fan`;`generic`];; searcht 5 [`wedge a b c d SUBSET wedge_ge a b c d`];; searcht 5 [name "EGHNAVX"];; searcht 10 [`local_fan`;`(x:real^3#real^3) IN FF`];; searcht 5 [`x = a,b`;`FST`;`SND`];; searcht 5 [`a,b = c,d`];; searcht 5 [`wedge_ge a b c d`;`wedge a b c d`];; searcht 5 [`convex_local_fan`;`local_fan`];; searcht 1 [`ITER`;`rho_node1`;`ivs_rho_node1`];; searcht 5 [`ITER 1`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types SKOLEM_EPSILON;; Print_types.print_term_types t';; bb 5;; (* July 8, 2013 *) searcht 5 [name "KOMW"];; searcht 5 [`x IN P hull s`];; searcht 5 [`aff_gt s t SUBSET affine hull u`];; searcht 5 [`ITER i (rho_node1 FF) w = ITER j (rho_node1 FF) w`];; searcht 5 [`local_fan`;`CARD V = CARD FF`];; searcht 5 [`ITER i (rho_node1 FF) v IN V`];; searcht 5 [`ITER (i+j)`];; searcht 5 [name "XIV"];; searcht 5 [`azim v0 v1 v2 v1`];; Local_lemmas.AZIM_SPEC_DEGENERATE;; searcht 5 [`azim v0 v1 v1 v2`];; searcht 5 [`azim v0 v1 v2 v3 + azim v0 v1 v3 v2`];; azim;; searcht 5 [`v IN wedge_ge a b c v`];; searcht 10 [`real_continuous`;`?`;`atreal`];; real_continuous_at;; searcht 5 [`dihV`;`real_continuous`];; searcht 5 [`(\t. c) continuous net`];; GSYM SKOLEM_EPSILON;; searcht 5 [`?d. (a /\ b d ==> c d)`];; searcht 5 [`azim`;`a IN aff_ge u v`];; searcht 5 [`azim a b c d = &0`;`&0 < x`];; searcht 5 [`SUC i = SUC j`];; searcht 15 [`azim`;`dihV`];; searcht 5 [`azim a b c d = &0`];; searcht 15 [`cyclic_set`;`%`];; searcht 5 [`t % e = vec 0`];; searcht 10 [`affine hull s`;`%`];; searcht 25 [`azim_cycle`;omit `FAN`;omit `azim_in_fan`;omit `local_fan`;omit `convex_local_fan`;omit `wedge_in_fan_gt`;`@`];; searcht 5 [`azim (vec 0) (t % e)`];; searcht 15 [`projection`;`%`];; Sphere.cyclic_set;; searcht 5 [`azim_cycle {x}`];; Sphere.azim_cycle;; searcht 5 [`collinear`;`cyclic_set`];; Wrgcvdr_cizmrrh.IDENTIFY_AZIM_CYCLE;; searcht 5 [`azim a (-- b) c d`];; searcht 15 [`%`;`continuous`];; searcht 5 [`wedge_in_fan_ge`];; Local_lemmas.LOCAL_FAN_CHARACTER_OF_RHO_NODE2;; deformation_rho_node1_equivariant1;; searcht 5 [`&0 < interior_angle1 u FF v`];; Local_lemmas.INTERIOR_ANGLE1_POS;; searcht 5 [`interior_angle1`;`azim`];; Nkezbfc_local.CONVEX_LOFA_IMP_INANGLE_EQ_AZIM_IVS;; searcht 5 [`rho_node1`;`ivs_rho_node1`];; searcht 5 [`ITER (a+b)`];; XIV_ECAU;; searcht 5 [`ivs_rho_node1 FF w IN V`];; searcht 5 [`ITER i (rho_node1 FF) w IN V`];; ITER;; searcht 5 [`ITER`;`rho_node1`;`ivs_rho_node1`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types SKOLEM_EPSILON;; Print_types.print_term_types t';; bb 4;; (* July 10, 2013 *) searcht 5 [`azim_in_fan`;`azim`];; searcht 5 [`v,rho_node1 FF v IN FF`];; PROPERTIES_GENERIC_LOCAL_FAN_ALT;; searcht 5 [`ITER i f w = ITER j f w`];; Local_lemmas1.LT_CARD_MONO_LOFA;; searcht 5[`ITER (CARD V - 1)`];; searcht 5[`ITER (CARD V)`];; searcht 5 [`ITER i (ivs_rho_node1 FF) v`;`ITER j (rho_node1 FF) v`];; searcht 5 [`collinear`;`ivs_rho_node1`];; searcht 5 [`rho_node1 FF v IN VV`];; searcht 5[`ITER i (ivs_rho_node1 FF) v IN V`];; searcht 5 [`ivs_rho_node1 FF (rho_node1 FF w)`];; searcht 5 [`rho_node1 FF (ivs_rho_node1 FF w)`];; XIV_ECAU;; KCZXLLE_SYM;; searcht 5 [`collinear`;`cross`];; searcht 15[`coplanar`;`affine hull s`];; searcht 15[`v2 IN affine hull {a,b,c}`;`%`;`vec 0`];; searcht 5 [`u1 cross u2 = -- (u2 cross u1)`];; searcht 15 [`&0 < x * y`];; searcht 2 [`&0 < x dot x`];; searcht 5 [`&0 < azim a b c d`;`azm a b c d = &0`];; searcht 5 [`azim a b c d = &0`;`aff_gt`];; searcht 5 [`collinear`;`%`];; searcht 5 [`e dot (e cross f)`];; searcht 5 [`azim a b c d <= azim a' b' c' d'`;`azim_cycle`];; searcht 5 [`azim_cycle U a b v IN U`];; searcht 5 [`aff_gt {a,b} {c}`;`%`];; searcht 5 [`DISJOINT`;`collinear`];; Polar_fan.AZIM_CYCLE_BASIC_PROPERTIES;; searcht 5 [`azim_cycle U o e v = v`];; searcht 5 [`azim a (-- e)`];; searcht 8 [`azim a b c d + azim a b d e`;omit `cyclic_set`];; searcht 5 [`&0 <= azim a b c d`];; searcht 50 [`azim`;`azim_cycle`];; Wrgcvdr_cizmrrh.AZIM_CYCLE_PROPERTIES;; searcht 15 [`s SUBSET affine hull t`];; searcht 5 [`aff_gt {a,b} {c}`;`%`];; AFF_GT_SUBSET_AFFINE_HULL;; searcht 5 [`periodic`;`ITER`];; searcht 5 [`local_fan`;`CARD FF = CARD V`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types SKOLEM_EPSILON;; Print_types.print_term_types t';; bb 4;; (* July 12, 2013 *) searcht 5 [name "A_482"];; searcht 5 [`MMs_v39`;`BBs_prime_v39`];; searcht 5 [`BBprime2_v39`;`BBprime_v39`];; Appendix.BBs_v39;; searcht 15 [`IMAGE f X SUBSET Y`];; searcht 5 [`local_fan`;`convex_local_fan`];; searcht 5 [`&0 < x`;`interior_angle1`];; searcht 5 [`IMAGE f (:A)`];; searcht 5 [`interior_angle1`;`azim`];; searcht 5 [`coplanar`;`azim_in_fan`];; searcht 5 [`rho_node1`;`is_scs_v39`];; searcht 5 [`ivs_rho_node1`;`is_scs_v39`];; searcht 5 [`ivs_rho_node1 FF u IN V`];; searcht 5 [`rho_node1 FF v = rho_node1 FF w`];; Qknvmlb.VV_SUC_EQ_RHO_NODE_PRIME;; searcht 5 [`rho_node1 FF (ivs_rho_node1 FF v)`];; searcht 5 [`generic`;`collinear`];; searcht 5 [`generic`;`scs_generic`];; searcht 5 [`is_scs_v39`;`&2 <= dist (v,u)`];; searcht 10 [`(p + a) MOD k = (p + b) MOD k`];; searcht 10 [`(a MOD k = a)`];; searcht 5 [`coplanar`;`azim`];; searcht 5 [`norm`;`ball_annulus`];; searcht 5 [`&0`;`delta_y`;`norm`];; Tame_lemmas.delta_y_pos;; rr[LET_DEF;LET_END_DEF] Tame_lemmas.delta_y_pos];; searcht 5 [`coplanar`;`delta_y`];; searcht 5 [`dist(vec 0,v)`;`norm`];; GSYM Oxlzlez.coplanar_delta_y;; searcht 5 [`&0 < x`;`ups_x`;`dist`];; Localization.deformation;; searcht 5 [`dist`;`~collinear {a,b,c}`;`x ==> ((u:real^3) = v)`;omit `cos`;omit `radV`];; searcht 5 [def "eqvl"];; searcht 5 [`coplanar`;`cross`];; Local_lemmas.NOT_COLL_IMP_COPL;; searcht 15 [`coplanar`;`%`];; Trigonometry2.NONCOPLANAR_3_BASIS;; searcht 5 [`v1 dot (v1 cross v2)`];; searcht 5 [`re_eqvl`];; searcht 5 [`cross`;`collinear`];; searcht 5 [`a dot a = &0`];; searcht 5 [`dist`;`norm`];; NORM_ADD_PYTHAGOREAN;; searcht 5 [`norm (t % v)`];; searcht 5 [`(norm x) pow 2`;`dot`];; searcht 5 [`t pow 2 = &1`];; searcht 5 [`t2 pow 2 = &0`];; searcht 5 [`(v1 cross v2) dot (v1 cross v2)`];; searcht 5 [name "CONTINUOUS_CONTINUOUS_WITHINREAL"];; Localization.deformation;; searcht 5 [`dist(a,b)= &0`];; searcht 5 [`collinear`;`coplanar`];; searcht 5 [`coplanar`;`~((v:real^A) = w)`];; searcht 5 [`coplanar`;`delta_y`;`dist`];; searcht 5 [`x pow 2 = y pow 2`];; searcht 5 [`&0 <= dist(x,y)`];; searcht 5 [`continuous`;`coplanar`];; searcht 5 [`dist(vec 0,v)`];; mk_simplex_uniq;; searcht 5 [`cross`;`azim`];; searcht 5 [`delta_y`;`norm`];; searcht 5 [`norm`;`dist`];; Oxlzlez.coplanar_delta_y;; REAL_CONTINUOUS_SUB;; REAL_CONTINUOUS_CONST;; ) orelse (mmp REAL_CONTINUOUS_NEG) orelse mmp REAL_CONTINUOUS_ABS) searcht 5 [`real_abs`;`real_continuous`];; ETA_AX;; REAL_CONTINUOUS_ABS;; searcht 5 [`I`;`real_continuous`];; searcht 5 [`(\x. x)`;` real_continuous`];; searcht 15 [`real_continuous`;`?`];; searcht 5 [`real_continuous`;`delta_x`];; searcht 5 [name "OPEN";name "REAL_INTERVAL"];; searcht 5 [`real_continuous`;`pow`];; DIST_0;; searcht 5 [`&0 < dist(x,y)`];; searcht 5 [`x pow 2 = y pow 2`];; searcht 5 [`&0 <= norm x`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types SKOLEM_EPSILON;; Print_types.print_term_types t';; bb 4;; (* July 12, 2013 *) searcht 5 [`a dot a`;`~(a = vec 0)`];; searcht 5 [`collinear {a,b}`];; searcht 5 [`coplanar`;`cross`];; searcht 5 [`collinear`;`cross`];; searcht 15 [`~coplanar {a,b,c,d}`;`%`];; VECTOR_SUB_RZERO;; searcht 15 [`coplanar`;`collinear`];; searcht 5 [`u IN affine hull {a,b,c}`;`%`];; searcht 5 [`x dot x = &0`];; searcht 5 [`norm (t % a)`];; searcht 5 [`norm v1`;`dot`];; searcht 10 [`a * b = c * b`];; searcht 5 [`n dot n = &0`];; searcht 5 [`a pow 2 = b pow 2`];; searcht 5 [`a % w = b % w`];; searcht 5 [`a * b = c * b`];; searcht 5 [`sqrt`;`real_continuous`];; searcht 5 [`continuous`;`cross`];; searcht 5 [`lift`;`continuous`];; searcht 5 [`real_continuous`;`(/)`];; searcht 5 [`collinear`;`ups_x`];; mk_planar2_continuous;; searcht 5 [`norm x = &0`];; searcht 5 [`&0 < ups_x a b c`;`dist`];; searcht 5 [`norm`;`dist`];; searcht 2 [`coplanar`;`~((u:real^3)=v)`];; mk_planar_unique;; searcht 5 [`~coplanar s`;`affine hull s`];; searcht 5 [`affine hull {a,u,v,w}`;`%`];; searcht 15 [`coplanar`;`%`;omit `~coplanar s`];; searcht 15 [`coplanar`];; searcht 20 [`coplanar`;`{a,b,c}`];; searcht 5 [`collinear`;`aff_dim`];; searcht 5 [`coplanar`;`aff_dim`];; searcht 5 [`aff_dim`;`s SUBSET t`];; searcht 5 [`x IN P hull s`];; searcht 5 [`affine hull {a,b,c}`;`%`];; searcht 2 [`&0 < v dot v`];; searcht 5 [`&0 < t * y <=> &0 < t`];; searcht 5 [`a % v = a % w`];; searcht 5 [`ups_x a b c = ups_x a' b' c'`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types SKOLEM_EPSILON;; Print_types.print_term_types t';; bb 5;; (* July 16, 2013 *) searcht 5 [`is_scs_v39 s`;`&2 <= dist(a,b)`];; searcht 5 [`(a + b) MOD k = (a + c) MOD k`];; searcht 15 [`(a MOD k = b MOD k)`;omit `5`;omit `3`;omit `is_scs_v39`];; searcht 5 [`a MOD k = a`];; searcht 5 [`{a,b}={c,d}`];; searcht 5 [`deformation`;`is_scs_v39`];; searcht 5 [def "ww_defor"];; searcht 5 [`convex_local_fan`;`deformation`;name ".ZLZ"];; frees_of_goal ([],`a b c`);; searcht 5 [name "SKOLEM_EPSILON"];; searcht 0 [`periodic`;`{(i:num) | i < k}`];; searcht 15 [`periodic2`;`0..u`];; searcht 15 [`periodic2`];; Oxl_def.periodic_numseg;; Terminal.periodic2_mod_reduce;; searcht 15 [`periodic2`];; SKOLEM_PERIODIC2;; searcht 5 [`is_scs_v39`;`3`];; help_grep "conj";; conjuncts `a /\ b /\ c`;; REWRITE_CONV [GSYM CONJ_ASSOC] `(a /\ b) /\ c`;; searcht 5 [name "Terminal";name "IMAGE"];; searcht 5 [`ball_annulus`;`norm`];; searcht 2 [`b_spine5`;`DECIMAL`];; searcht 5 [`dist`;`real_continuous`];; searcht 5 [`IMAGE f (IMAGE g X)`];; searcht 5 [`IMAGE f (a INSERT s)`];; searcht 5 [`generic`;`scs_generic`];; searcht 50 [`interior_angle1`;`azim`];; searcht 5 [`deformation`;`interior_angle1`];; searcht 5 [`azim_in_fan`;`azim`];; searcht 5 [`azim_in_fan`;`azim`];; searcht 5 [`azim_in_fan`;`interior_angle1`];; searcht 5 [`interior_angle1`;`azim`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types SKOLEM_EPSILON;; Print_types.print_term_types t';; bb 8;; (* July 17, 2013 *) searcht 5 [`deformation`;`local_fan`];; searcht 5 [`is_scs_v39`;`i + (k-1)`];; searcht 5 [`convex_local_fan`;`local_fan`];; Ocbicby.INTERIOR_ANGLE1_AZIM;; named "azim_in_fan2";; named "EXISTS_INVERSE_OF_V";; map named[ "LOFA_IMP_EE_TWO_ELMS"; "LOFA_CARD_EE_V_1"; "LOCAL_FAN_RHO_NODE_PROS2";];; Local_lemmas.azim_in_fan2;; searcht 5 [`rho_node1`;`vv (SUC i)`];; searcht 5 [`is_scs_v39`;`(!i j. i < k /\ j < k /\ v i = v j ==> i = j)`];; searcht 5 [`is_scs_v39`;`&2 <= dist(a,b)`];; searcht 5 [`i MOD k = i`];; searcht 5 [`ivs_rho_node1`;`vv (i + (k-1))`];; searcht 5 [`interior_angle1`;`azim`;`is_scs_v39`];; Ocbicby.INTERIOR_ANGLE1_AZIM;; GSYM (REWRITE_RULE[LET_DEF;LET_END_DEF;arith `SUC i = i+1`] Ocbicby.INTERIOR_ANGLE1_AZIM);; searcht 5 [`cross`;`azim `;`&0 < x`];; deform_simplex_edge_exists;; searcht 5 [`{a,b} = {c,d}`];; searcht 5 [`(\t .t) real_continuous net`];; searcht 5 [name "periodic2";name "reduce"];; searcht 5 [`periodic2`;`MOD`];; searcht 5 [`periodic`;`MOD`];; searcht 5 [`i MOD k < k`];; searcht 0 [`(i + k) MOD k`];; searcht 5 [`(a*b+c) MOD k`];; searcht 5 [`j MOD k = j`];; searcht 5 [name "split";name "generic"];; searcht 15 [`azim a b c d + azim a' b' c' d'`;name "3"];; searcht 5 [name "tau_fun_azim"];; searcht 5 [`scs_generic`;`generic`];; searcht 5 [`azim a b c d < &2 * pi`];; searcht 5 [`collinear`;`azim`;omit `~collinear s`];; searcht 5 [`I x = x`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types SKOLEM_EPSILON;; Print_types.print_term_types t';; bb 6;; (* July 18, 2013 *) searcht 5 [`psort`];; searcht 5 [`(a,b) = (c,d)`];; searcht 5 [`(a*b + c) MOD k`];; searcht 5 [`dist(a,b) + dist(b,c)`];; searcht 5 [`ball_annulus`;`norm`];; searcht 5 [name "IMAGE_SUBSET";name "IN"];; searcht 5 [`(a + b) MOD k`;`(a MOD k + b MOD k) MOD k`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types SKOLEM_EPSILON;; Print_types.print_term_types t';; bb 10;; (* July 19, 2013 *) searcht 10 [`azim`;`real_continuous`];; searcht 5 [`generic`;`collinear`];; searcht 5 [`local_fan`;`convex_local_fan`];; searcht 5 [`(a + c) MOD k = (a + c') MOD k`];; searcht 5 [`deformation`;`collinear`];; searcht 5 [name "continuous_nbd_pos"];; searcht 5 [`azim`;`aff_ge`];; searcht 5 [`&0 < azim a b c d`;`~(azim a b c d = &0)`];; searcht 5 [`azim a b c d = &0`;`coplanar`];; searcht 5 [`azim`;`convex_local_fan`;`i + k - 1`];; searcht 5 [`atn x < atn y`];; searcht 10 [`coplanar`;`collinear`;`( /\ )`];; searcht 5 [`sin x`;`&0 < x /\ x < pi`];; searcht 5 [`azim a b c d < &2 * pi`];; searcht 5 [`re_eqvl`;`sin`];; searcht 5 [`re_eqvl`;`&0 < x`];; searcht 15 [`azim`;`dihV`];; AZIM_DIHV_SAME;; searcht 5 [`pi / &2 `;`dih_x `];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types CONTINUOUS_LIFT_DOT2 ;; Print_types.print_term_types t';; bb 10;; back_to "CVX_LO_IMP";; (* July 20, 2013 *) searcht 5 [`dihV`;`dih_x`];; searcht 8 [name "REAL_MVT"];; searcht 5 [`derived_form`;`dih_x`;`delta_x6`];; HAS_REAL_DERIVATIVE_TRANSFORM_WITHIN;; searcht 5 [`f'`];; searcht 5 [`net within (:real)`];; searcht 5 [`net within s`;`(f has_real_derivative f') (atreal x)`];; searcht 5 [`net within s`;`f real_continuous (atreal x)`];; searcht 5 [`(f o g) has_real_derivative f'`];; searcht 5 [`dih_x`;`delta_x4`];; searcht 5 [`real_continuous`;`delta_x`];; searcht 5 [`(\t. -- f t) real_continuous net`];; REAL_CONTINUOUS_SUB;; searcht 5 [`(\t. t) real_continuous net`];; searcht 5 [`dih_x a b c d e f <= dih_x a b c d' e' f'`];; Tame_inequalities.DIH_X_MONO_LT_4;; searcht 5 [`delta_x5`;`delta_x6`];; searcht 5 [`dih_x a b c d e f = dih_x a c b d' e' f'`];; searcht 5 [`&0 < ups_x a b c`;`collinear`];; searcht 5 [`pi / &2 < dih_x a b c d e f`;`delta_x4`];; searcht 5 [`coplanar {a,b,c}`];; searcht 3 [`&0 < delta_y a b c d e f`;`dist`];; searcht 5 [`real_min`];; searcht 5 [`abs`;`real_continuous`];; dihV_obtuse_mono_a;; searcht 5 [name "CONTINUOUS_AT_LIFT_DOT2"];; searcht 5 [`dihV a b c d = dihV a b d c`];; searcht 15 [`abs`;`real_continuous`];; searcht 5 [`(\u. u)`;`real_continuous`];; Searching.searcht 5 [name "CONTINUOUS_LIFT_DOT"];; g `!net f i. f continuous net /\ g continuous net ==> (\x. lift (f x dot g x)) continuous net`;; searcht 5 [name "SYNQ"];; Searching.searcht 5 [name "REAL_CONTINUOUS_ATREAL_DIHV_COMPOSE"];; Searching.searcht 5 [`lift`;`continuous`;`real_continuous`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types CONTINUOUS_LIFT_DOT2 ;; Print_types.print_term_types t';; bb 4;; back_to "kill";; (* July 22, 2013 *) searcht 5 [`interior_angle1`;`azim`;`i + k - 1`];; searcht 5 [`psort k (a,b) = psort k (b,a)`];; searcht 5 [`psort k (a MOD k,b)`];; searcht 5 [`(a MOD k) MOD k`];; searcht 5 [`scs_a_v39`;`MOD`];; searcht 50 [def "tau"];; searcht 15 [`taustar_v39`;`tau_fun`];; searcht 5 [`tau_fun`;`azim`];; searcht 5 [`BBs_v39`;`periodic`];; searcht 5 [`dsv_v39`];; Appendix.is_basic;; searcht 50 [`is_basic`];; searcht 5 [`sum (A DIFF B)`];; searcht 5 [`tau3`;`taum`];; searcht 5 [`tau3`;`dihV`];; searcht 5 [`FINITE {i | (i:num) < k}`];; searcht 5 [`sum A f = sum A g`];; searcht 5 [`sum {a,b,c} f`];; searcht 15 [`(a + b) MOD k`;omit `5`];; MOD_ADD_MOD;; DIVISION;; searcht 5 [`0 MOD k`;omit `a MOD 4`];; searcht 5 [`x MOD k = x`];; MOD_SHIFT;; searcht 5 [`(a + c) MOD k = (a + b) MOD k`];; searcht 5 [`taum`;`tau3`];; searcht 15 [`azim`;`dihV`];; searcht 5 [name "FSQ"];; searcht 5 [`real_interval (a,b)`;`abs t`];; Zlzthic.real_interval_contains_0_ball;; searcht 5 [`rho`;`rho_fun`];; MOD_SHIFT;;s searcht 5 [`taum a b c d e f = taum a' b' c' d' e' f'`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types CONTINUOUS_LIFT_DOT2 ;; Print_types.print_term_types t';; bb 4;; back_to "kill";; (* July 23, 2013 *) searcht 5 [name "deform_simplex_684"];; searcht 5 [`coplanar`;`cross`;`dot`];; searcht 5 [`azim`;`cross`;`dot`];; searcht 5 [`re_eqvl`;`&0 < x`];; searcht 5 [`re_eqvl`;name "SYM"];; searcht 5 [def "quadratic"];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types CONTINUOUS_LIFT_DOT2 ;; Print_types.print_term_types t';; bb 4;; back_to "kill";; (* July 24, 2013 *) searcht 15 [`quadratic_root_plus`];; searcht 5 [name "2x2"];; searcht 25 [`real_sgn`];; searcht 5 [`real_sgn(x * y)`];; searcht 5 [`real_sgn x = &1`];; GSYM REAL_SGN_EQ;; searcht 5 [`real_sgn`;`abs`];; searcht 5 [`y / x = &0`];; searcht 15 [`&0 < x * y`];; searcht 5 [`re_eqvl`;`&0 <= x`];; searcht 5 [`sin`;`azim`];; searcht 5 [`coplanar`;`delta_y`];; Collect_geom2.POS_EQ_NOT_COPLANANR;; searcht 5 [`&0 <= delta_y a b c d e f`;`dist`];; searcht 5 [`delta_x`;`abc_of_quadratic`];; searcht 5 [`delta_x`;`a * u pow 2 + b * u + c`];; searcht 5 [`convex`;`real_interval`];; searcht 5 [`FINITE`;`connected`];; CONTINUOUS_FINITE_RANGE_CONSTANT;; Localization.deformation;; searcht 5 [`convex`;`connected`];; searcht 5 [`real_interval`;`interval`];; searcht 5 [`real_interval`;`real_connected`];; searcht 5 [`real_continuous`;`FINITE`];; searcht 5 [def "kepler"];; searcht 5 [`kepler_conjecture`;`saturated`;`packing`];; searcht 5 [`drop (lift x)`];; searcht 15 [`f x IN IMAGE f X`];; searcht 5 [`lift`;`real_interval`];; searcht 5 [`connected`;`interval`];; searcht 5 [`continuous_on`;`real_continuous_on`];; ETA_AX;; searcht 5 [`IMAGE f (IMAGE g X)`];; searcht 5 [`drop o lift`];; searcht 5 [`real_continuous`;`dist`];; searcht 5 [`real_continuous`;`real_continuous_on`];; searcht 5 [`real_open`;`real_interval(a,b)`];; FINITE_SUBSET;; searcht 5 [`FINITE`;`INSERT`];; searcht 15 [`IMAGE f X`;`HAS_SIZE`];; searcht 5 [`azim a b c d = &0`;`cross`];; searcht 5 [`interior_angle1`;`azim_in_fan`];; searcht 15 [`azim_in_fan`;`azim`];; searcht 5 [`interior_angle1`;`BBs_v39`];; Ocbicby.INTERIOR_ANGLE1_AZIM;; searcht 5 [`&0 < azim a b c d`;`convex_local_fan`];; searcht 5 [`5 MOD 5`];; Appendix.scs_diag;; searcht 5 [`(a /\ c) \/ (a /\ b)`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas.EGHNAVX;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 5;; back_to "azim 0";; (* July 25, 2013 *) searcht 5 [name "EGH"];; searcht 5 [` IMAGE (\i. (v i,v (SUC i))) (:num)`;`rho_node1`];; searcht 5 [name "FEKT"];; searcht 5 [`coplanar`;`&0`;`pi`;`azim`];; type_of `scs_basic_v39`;; searcht 15 [`CARD`;`is_scs_v39`];; searcht 5 [`collinear`;`generic`];; searcht 5 [`scs_generic`;`generic`];; help "GEN_ALL";; help "GENL";; searcht 15 [`(!i. a ==> P i)`;`a ==> (!i. P i)`;name "FORALL"];; searcht 5 [name "FORALL";name "AND"];; (GSYM Ocbicby.INTERIOR_ANGLE1_AZIM);; searcht 5 [`aff_gt {a,b} {c}`;`%`];; searcht 5 [`i MOD k < k`];; searcht 5 [name "SHIFT";`(a + b) MOD k = (a + c) MOD k`];; searcht 5 [`i MOD k = i`];; searcht 5 [`cross`;`collinear`];; searcht 5 [`coplanar`;`affine hull s`];; searcht 5 [`x IN P hull s`];; searcht 5 [`periodic`;`IMAGE`;`a..b`];; searcht 5 [`periodic`;`a..b`];; searcht 5 [`aff_gt s t SUBSET affine hull s'`];; searcht 5 [`collinear`;`affine hull s`;`SUBSET`];; AFFINE_HULL_3_GENERATED;; searcht 5 [`coplanar`;`affine hull s`];; AFFINE_HULL_3_GENERATED;; Terminal.vv_split_azim_generic;; searcht 5 [`&0 <= azim a b c d`];; Local_lemmas1.AZIM_COND_FOR_COPLANAR;; searcht 5 [`real_continuous`;`azim a b c d < x`];; WNWSHJT_ALT;; searcht 5 [`coplanar`;`collinear`;`/\`];; searcht 5 [`azim`;name "fan3"];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 3;; back_to "deform coll";; (* July 27, 2013 *) searcht 10 [`dihV`;`azim`;name "STRONG"];; searcht 5 [`dihV`;`dih_x`];; searcht 5 [`collinear`;`ups_x`];; searcht 5 [name "SYN"];; searcht 5 [def "xrr"];; searcht 5 [`xrr`;`&1`];; Appendix.scs_v39;; searcht 5 [`dest_scs_v39`];; searcht 5 [`FST x = FST x'`];; searcht 5 [`part1`];; searcht 5 [name "EGH"];; searcht 5 [`s SUBSET P hull s`];; searcht 5 [`aff_gt s t SUBSET affine hull t'`];; searcht 5 [`convex_local_fan`;`interior_angle1`];; searcht 5 [`azim`;`dot`;`cross`];; searcht 5 [`re_eqvl`;`&0 < x`;`==>`];; searcht 5 [`&0 < sin x`;`azim`];; searcht 5 [`abs`;`real_continuous`];; a5_assumption_reduction;; searcht 5 [name "nbd_pos"];; searcht 5 [`is_scs_v39`;`&2 <= scs_a_v39 s i j`];; searcht 5 [`dist`;`real_continuous`];; Local_lemmas1.CON_ATREAL_REAL_CON;; type_of `t0`;; searcht 50 [`t0`];; searcht 50 [`quarter`];; searcht 50 [`quasi_tri`];; searcht 15 [`collinear`;`continuous`];; searcht 15 [`collinear`;`deformation`];; searcht 5 [`azim`;`dih_y`];; Cuxvzoz.deform_684_pent_exists;; searcht 5 [name "FSQK"];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 3;; back_to "epsilon_hex";; (* July 27, 2013 *) searcht 3 [`azim`;`dih_y`];; searcht 5 [`coplanar`;`azim`;`pi`;`&0`];; searcht 5 [`&0 < azim a b c d`;`abs t < e`];; searcht 5 [`deformation`;`subset`];; searcht 5 [name "WNW"];; searcht 5 [`dih_y a b c d e f <= dih_y a b c d' e f`];; Ocbicby.dih_y_mono;; searcht 5 [`continuous`;`coplanar`];; azim_dih_y;; searcht 5 [`&0 < norm x`];; searcht 5 [`~coplanar s`;`~(x = y)`;`/\ `];; searcht 5 [`delta_y a b c d e f`;`coplanar`];; searcht 5 [`delta_y a b c d e f = delta_y a' b' c' d' e' f'`];; searcht 5 [`&0 <= delta_y a b c d e f`];; searcht 25 [`sum (a..b)`];; SUM_4;; searcht 5 [`sum (0..4)`];; searcht 5 [`sum (a..b)`;`sum ((SUC n)..b)`];; searcht 5 [`sum (0..3)`];; searcht 5 [name "sym";`xrr`];; searcht 5 [`ball_annulus`;`norm`];; searcht 5 [`taum`;`tau3`];; Cuxvzoz.tau3_taum_nonplanar;; searcht 5 [`tau3`;`azim`];; Cuxvzoz.tau3_azim;; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 3;; back_to "COMMENT";; (* July 29, 2013 *) searcht 5 [`taum a b c d e f = taum a' b' c' d' e' f'`];; searcht 5 [`arclength a b c + arclength a' b' c'`];; searcht 12 [`arcV u v w + arcV u' v' w'`];; searcht 15 [`arclength`;`aff_gt`];; searcht 5 [`angle s + angle s'`];; ANGLES_ADD_AFF_GE;; searcht 5 [`angle`;`arcV`];; Nkezbfc_local.PROPERTIES_GENERIC_LOCAL_FAN;; searcht 5 [`DISJOINT`;`collinear`];; searcht 5 [`DISJOINT`;name "SYM"];; Qknvmlb.VV_SUC_EQ_RHO_NODE_PRIME;; Local_lemmas.LUNAR_IMP_HALF_CIRCLE_SUBSET_AFF_GT;; Local_lemmas.LOCAL_FAN_CHARACTER_OF_RHO_NODE2;; Planarity.decomposition_planar_by_angle_fan;; Planarity.POINT_IN_AFF_GE_IMP_IN_EDGE;; searcht 5 [name "WL_IN_E"];; searcht 5 [`FAN`;`aff_ge`];; searcht 5 [`FAN`;`local_fan`];; searcht 5 [`FAN`;`{a,b} IN E`;`~(a = b)`];; searcht 5 [`arclength`;`atn`];; searcht 5 [`xrr`;`arclength`];; searcht 5 [`acs`;`pi`;`cos`];; searcht 5 [`cos z < &1`];; searcht 5 [`cos (z+pi)`];; searcht 5 [`cos (-- z)`];; searcht 5 [`sqrt x * sqrt x = x`];; seracht 5 [`xrr a b c <= d`];; searcht 5 [`arclength`;`acs`];; searcht 5 [`(a * a + b * b - c*c)/(&2 * a*b)`;`<=`];; Oxl_2012.GRHIDFA;; searcht 5 [`cc_card_v11`;`CARD`];; searcht 5 [`gg_mcell`;`cc_gg_v11`];; searcht 5 [`cell_cluster_estimate_v1`];; searcht 5 [`TSKAJXY_statement`];; searcht 10 [name "TSKAJXY"];; searcht 5 [name "Zorn"];; searcht 5 [`delta4_squared_y`;`x1_delta_y`];; searcht 15 [`hminus`;`DECIMAL`];; searcht 5 [`const1`;`pi`];; searcht 5 [`sol0`;`DECIMAL`];; Flyspeck_constants.bounds;; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 3;; back_to "RIGHT_FORALL";; (* Aug 4, 2013 *) searcht 5 [`delta_x4`;`dih_x`];; searcht 5 [`ups_x (a*a)`;`a*b*c`];; searcht 5 [`&0 < x * y <=> &0 < y`];; Sphere.delta4_y;; Sphere.delta_y;; searcht 5 [`atn2 (x,y)`;`x < y`];; searcht 5 [`atn x < pi / &2`];; searcht 5 [`atn (-- x)`];; DIST_TRIANGLE;; searcht 5 [`&0 <= delta_y y1 y2 y3 y4 y5 y6`;`dist`];; searcht 5 [`cos`;`acs`;`pi`];; searcht 5 [`sqrt x * sqrt x`];; searcht 5 [`x pow 2 <= y pow 2`];; searcht 5 [`abs x pow 2`];; searcht 5 [name "1834"];; searchl ineq_as_thm [`[(&2,y1,&2*h0);(&2,y2,&2*h0);(&2,y3,&2*h0);(&2,y4,&2*h0);(&2,y5,&2*h0);(&2,y6,&2*h0)]`];; searcht 5 [`compact`;`real_continuous_on`];; searcht 5 [`derived_form`;`dih_x`];; searcht 5 [`taum`;`dih_x`];; searcht 5 [`taum`;`dih_y`];; Sphere.taum;; searcht 5 [`taum`;`rhazim`];; Sphere.rhazim;; searcht 5 [`arclength`;`xrr`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 4;; back_to "periodic2_mod_reduce";; (* Aug 4, 2013 *) searcht 5 [`rho`;`ly`];; searcht 5 [`sol0`;`const1`];; searcht 5 [`real_continuous`;`dih_y`];; searcht 15 [`f o g`;`real_continuous`];; searcht 5 [`(\t. t) real_continuous net`];; searcht 5 [`real_continuous`;`has_real_derivative`];; searcht 5 [`ups_x a b c = ups_x b a c`];; searcht 5 [`real_compact`;`real_interval [a,b]`];; searcht 5 [`real_continuous_on`;`real_continuous`];; searcht 15 [`&0 < ups_x a b c`];; searcht 5 [`c <= xrr a b d`];; searcht 5 [`xrr a b c <= d`];; searcht 5 [`&0 <= taum y1 y2 y3 y4 y5 y6`];; searcht 5 [`c <= sqrt8`;`h0`];; searcht 5 [`d_tame i = j`];; searcht 5 [`scs_arrow_v39`;`scs_6I1`];; searcht 5 [name "EAPG"];; searcht 5 [`CONS a b = CONS a' b'`];; searcht 26 [`s_init_list_v39`;`scs_6I1`];; searcht 5 [name "periodic2";name "red"];; searcht 5 [`funlist_v39`;`periodic2`];; searcht 5 [`(i+k) MOD k`];; searcht 5 [`{a,b} = {c,d}`];; searcht 5 [`psort 5 (0,2)`];; Ocbicby.psort_5;; searcht 5 [`scs_arrow_v39`;`MMs_v39`];; searcht 5 [name "OTMT"];; searcht 5 [`is_scs_v39`;`scs_3T1`];; searcht 5 [`BBs_v39`;`MMs_v39`];; searcht 5 [`~(x = {})`;`?`];; searcht 5 [`scs_basic_v39`;`scs_3T5`];; searcht 5 [`mk_unadorned_v39`;name "explicit"];; searcht 5 [`BBs_v39`;`MMs_v39`];; searcht 5 [`psort 3 (0,1)`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 7;; back_to "Cuxv";; (* Aug 6, 2013 *) searcht 5 [`5 MOD 4`];; Cuxvzoz.deform_simplex_edge_exists;; searcht 5 [`coplanar`;`azim`;`pi`;`&0`];; searcht 5 [name "coplanar_cross_reduction"];; searcht 20 [`azim`;`cross`;`dot`];; searcht 15 [`coplanar`;`collinear`;`/\`];; searcht 15 [`{a,b,c,d} = {a',b',c',d'}`];; searcht 5 [`p MOD k < k`];; searcht 5 [`((a MOD k) + b) MOD k`;omit `5`];; searcht 5 [`(a + b) MOD k = (a + b') MOD k`];; searcht 5 [`p MOD k MOD k`];; searcht 5 [`3 MOD 4`];; searcht 5 [`scs_diag k p q`];; searcht 5 [name "SKOLEM_EPSILON"];; searcht 5 [name "SKOLEM";name "PERIODIC"];; searcht 5 [`&0 < azim a b c d`;`deformation`];; searcht 5 [`deformation`;`SUBSET`];; searcht 5 [name "epsilon_quad"];; searcht 5 [`collinear`;`ups_x`];; help "RAND_CONV";; help "RATOR_CONV";; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 5;; back_to "STRONG";; (* Aug 8, 2013 *) searcht 5 [`convex_local_fan`;`interior_angle1`;`pi`];; Cuxvzoz.WNWSHJT_ALT;; UNDISCH Ocbicby.LEMMA_1834976363;; searcht 50 [`azim`;`+`;`deformation`];; Localization.deformation;; searcht 5 [name "WNW"];; searcht 15 [`~collinear s`;`continuous`];; searcht 15 [`azim a b c d + azim a b d e`;`pi`;name "fan"];; searcht 50 [`(azim a b c d) < pi `];; searcht 5 [`d <= xrr a b c`];; searcht 5 [`xrr a b c <= d`];; searcht 5 [`&2 <= dist s`;`BBs_v39`];; searcht 5 [`sqrt(x pow 2)`];; searcht 15 [`x <= sqrt y`];; searcht 5 [`coplanar`;`delta_y`];; searcht 5 [`coplanar`;`collinear`;`/\`];; searcht 5 [name "SUM_NUMSEG3"];; Cuxvzoz.MMs_minimize_tau_fun;; searcht 5 [`periodic`;`sum`];; searcht 15 [`sum (a..b)`;`SUC`];; searcht 5 [`sum (p..p)`];; searcht 5 [`interior_angle1`;`azim`;`is_scs_v39`];; REWRITE_RULE[LET_THM] Ocbicby.INTERIOR_ANGLE1_AZIM;; searcht 5 [`(p + k) MOD k`];; searcht 5 [name "LEMMA_684"];; searcht 5 [`(p+k) MOD k`];; searcht 5 [`i MOD k = i`];; searcht 5 [`delta4_y`;`dih_y`];; searcht 5 [`dihV`;`dih_y`];; searcht 3 [`&0 <= delta_y a b c d e f`;`dist`];; searcht 5 [`azim`;`dihV`;name "STRONG"];; searcht 5 [`dihV`;`dih_y`];; Merge_ineq.DIHV_EQ_DIH_Y;; searcht 5 [`dih_y a b c d e f <= dih_y a b c d' e f`];; searcht 5 [`arclength`;`atn`];; searcht 15 [`sqrt x < y`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 3;; back_to "edge lengths";; (* Aug 11, 2013 *) searcht 5 [`coplanar`;`azim`];; searcht 3 [`is_scs_v39`;`&0 < azim a b c d`];; searcht 5 [`&0 < delta_y a b c d e f`;`coplanar`];; searcht 5 [`dih_y a b c d e f = dih_y a' b' c' d' e' f'`];; searcht 5 [`x1_delta_y`];; Trigonometry2.NOT_ZERO_EQ_POW2_LT;; searcht 5 [`&0 <= delta_y a b c d e f`;`dist`];; searcht 5 [`hypermap_of_list`];; searcht 15 [`hypermap_of_list`];; searcht 5 [name "lemma";name "merge"];; searcht 5 [name "planar_hypermap"];; searcht 5 [name "TGJ"];; searcht 5 [name "samsara"];; type_of `is_inj_list`;; searcht 5 [name "ThreeDarts"];; searcht 5 [name "is_loop"];; searcht 5 [`x:(A) loop`];; searcht 5 [name "iso";`iso`];; searcht 5 [name "Quotient"];; searcht 15 [name "lemmaNodalFixedPoint"];; searcht 5 [`is_no_double_joins`];; Hypermap.cycle;; searcht 5 [name "dih2k"];; Hypermap.lemma_mInside;; Hypermap.lemmaHQYMRTX;; searcht 50 [def "tame"];; type_of `bn_cong_iso`;; searcht 5[name "hypermap_of_list"];; searcht 15 [`hypermap_of_list`];; List_hypermap.good_list;; searcht 5 [`MAP I`];; searcht 5 [`IMAGE I`];; searcht 15 [`good_list`;`hypermap_of_list`];; searcht 5 [name "perm_eq"];; searcht 15 [`perm_eq`];; searcht 5 [`dropl 0`];; searcht 5 [`cat s []`];; searcht 5 [`acs`;`atn`];; searcht 5 [`kepler_conjecture`;`packing`];; searcht 5 [name "OEHDBEN"];; let nd s = searcht 5 [name s];; map nd ["OEHDBEN";"OTMTOTJ1";"OTMTOTJ3"];; map nd ["CNICGSF"];; map nd ["FYSSVEV";"ARDBZYE";"AUEAHEH";"VQFYMZY"];; map nd ["VQFYMZY"];; map nd ["BNAWVNH";"RAWZDIB";"MFKLVDK";"RYPDIXT"];; map nd ["NWDGKXH";"YOBIMPP";"MIQMCSN";"BKOSSGE"];; searcht 5 [`sin (x + y) = sin x`];; open Counting_spheres;; open Tactics_jordan;; open Ysskqoy;; open Hales_tactic;; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 3;; back_to "edge lengths";; (* Aug 15, 2013 *) searcht 5 [`delta`;`delta_x`];; searchd [`delta`];; searcht 5 [`b_coef`];; searchd [`d3`];; searcht 5 [`voronoi_trg`];; searcht 5 [`voro2`];; searcht 5 [`voronoi_open`];; searchd [`cm3_ups_x`];; searcht 5 [`cm3_ups_x`];; searcht 5 [`condA`];; List.length (definitions());; searchd [`rho_ij`];; searcht 5 [`rho_ij`;`rho_x`];; searcht 15 [`chi`];; searcht 5 [`the`];; searcht 20 [`SOME x`];; searcht 5 [`concat`];; searcht 5 [`filter`;`FILTER`];; searcht 5 [`filter`;`CONS`];; searcht 5 [`f (CONS (x:A list) xs) = APPEND x (concat xs)`];; searcht 5 [`MAP`;`map`];; type_of `minimal`;; searcht 50 [def "MIN"];; searchd [`MIN`];; searchd [`minn`];; searcht 50 [`minn`];; searcht 5 [`set_of_list []`];; searcht 5 [`POWER`;`ITER`];; let s1 t = searcht 5 [t];; s1 `min_num`;; searcht 5 [`min_num`;`INSERT`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 3;; back_to "edge lengths";; (* Aug 15, 2013 *) Misc_defs_and_lemmas.min_least;; searcht 5 [`MIN`];; searcht 5 [`minn x y <= x`];; searcht 5 [`set_of_list`;`{}`];; Seq.filter;; searcht 5 [`dropl (SUC n)`];; Seq.take;; SPEC_TAC;; searcht 5 [`x ++ []`];; Seq.rot;; searcht 5 [`sol_euler_x`;`delta_x`];; searchd [`dih4_x`];; searcht 50 [`mardih6_x`];; searcht 50 [`dih4_x`];; searcht 50 [`domain6`];; searcht 10 [`gamma3f_x_div_sqrtdelta`];; print_proof();; Print_types.print_goal_types();; Print_types.print_thm_types Local_lemmas1.CON_ATREAL_REAL_CON;; Print_types.print_term_types t';; frees (concl Local_lemmas.EGHNAVX);; bb 3;; back_to "edge lengths";; (* Aug 19, 2013 *) searcht 10 [`ldih6_x`];; searchp [`vol3f_x_sqrt2_lmplus`];; searchp [`arclength_x_123`];; Nonlin_def.vol3f_x_sqrt2_lmplus;; Sphere.rhazim_x;; searcht 5 [name "sq_pow2"];;