1 (* Extension of snapshot.hl. This has to be read in after the flyspeck build,
2 because it contains new types defined by the build *)
4 module Snapshot_flyspeck_build_2010_02_12 : Snapshot_type = struct
6 let hol_version = "2.20++";;
7 let hol_snapshot = "7_31_09";;
8 let svn_version = 1524;;
10 let the_interface = Snapshot_v220_7_31_2009.the_interface;;
11 let the_filetable = [("general/flyspeck_utility.hl", 832);
12 ("general/update_database_310.ml", 832); ("hypermap/hypermap.hl", 832);
13 ("volume/vol1.hl", 737); ("trigonometry/trigonometry.hl", 719);
14 ("general/flyspeck_utility.hl", 717); ("trigonometry/trig2.hl", 717);
15 ("trigonometry/trig1.hl", 708); ("nonlinear/ineqdata3q1h.hl", 707);
16 ("nonlinear/ineq.hl", 707); ("leg/enclosed_def.hl", 707);
17 ("leg/quadratic_root_plus_def.hl", 706);
18 ("leg/abc_of_quadratic_def.hl", 705); ("leg/muR_def.hl", 704);
19 ("leg/collect_geom.hl", 703); ("leg/cayleyR_def.hl", 678);
20 ("leg/affprops.hl", 677); ("leg/AFF_SGN_TAC.hl", 677);
21 ("leg/geomdetail.hl", 677); ("pervasives", 673)];;
25 ("map3", `:real^3->real^3->real^3`);
26 ("canon", `:(A)hypermap->((A)loop->bool)->((A->bool)->bool)->bool`);
27 ("is_flag", `:(A)hypermap->((A->bool)->bool)->bool`);
28 ("is_gen_flag", `:(A)hypermap->(A->bool)->((A->bool)->bool)->bool`);
29 ("edge_nondegenerate", `:(A)hypermap->bool`);
30 ("face_collection", `:(A)hypermap->(A)loop->bool`);
31 ("face_loop", `:(A)hypermap->A->(A)loop`);
32 ("res", `:(A->A)->(A->bool)->A->A`);
33 ("team", `:(A)hypermap->(A)loop->(A->bool)->bool`);
34 ("iso", `:(A)hypermap->(B)hypermap->bool`);
35 ("quotient", `:(A)hypermap->((A)loop->bool)->(A->bool)hypermap`);
36 ("nmap", `:(A)hypermap->((A)loop->bool)->(A->bool)->A->bool`);
37 ("fmap", `:(A)hypermap->((A)loop->bool)->(A->bool)->A->bool`);
38 ("tail", `:(A)hypermap->((A)loop->bool)->A->A`);
39 ("head", `:(A)hypermap->((A)loop->bool)->A->A`);
40 ("choice", `:(A)hypermap->((A)loop->bool)->A->A->bool`);
41 ("support_darts", `:((A)loop->bool)->A->bool`);
42 ("quotient_darts", `:(A)hypermap->((A)loop->bool)->(A->bool)->bool`);
43 ("is_normal", `:(A)hypermap->((A)loop->bool)->bool`);
44 ("atom", `:(A)hypermap->(A)loop->A->A->bool`);
45 ("is_node_going", `:(A)hypermap->(A)loop->A->A->bool`);
46 ("in_path", `:(num->A)->num->A->bool`);
47 ("set_dart_of", `:(num->A)->num->A->bool`);
48 ("contour_of", `:(A)loop->A->num->A`);
49 ("is_loop", `:(A)hypermap->(A)loop->bool`); ("top", `:(A)loop->num`);
50 ("size", `:(A)loop->num`); ("inside", `:A->(A)loop->bool`);
51 ("back", `:(A)loop->A->A`); ("next", `:(A)loop->A->A`);
52 ("dart_of", `:(A)loop->A->bool`);
53 ("tuple_loop", `:(A)loop->(A->bool)#(A->A)`);
54 ("loop", `:(A->bool)#(A->A)->(A)loop`);
55 ("shift_path", `:(num->A)->num->num->A`);
56 ("is_Moebius_contour", `:(A)hypermap->(num->A)->num->bool`);
57 ("is_splitting_component", `:(A)hypermap->A->bool`);
58 ("planar_ind", `:(A)hypermap->real`);
59 ("is_face_split", `:(A)hypermap->A->bool`);
60 ("is_node_split", `:(A)hypermap->A->bool`);
61 ("is_edge_split", `:(A)hypermap->A->bool`);
62 ("is_face_merge", `:(A)hypermap->A->bool`);
63 ("is_node_merge", `:(A)hypermap->A->bool`);
64 ("is_edge_merge", `:(A)hypermap->A->bool`);
65 ("inj_orbit", `:(A->A)->A->num->bool`);
66 ("double_face_walkup", `:(A)hypermap->A->A->(A)hypermap`);
67 ("double_node_walkup", `:(A)hypermap->A->A->(A)hypermap`);
68 ("double_edge_walkup", `:(A)hypermap->A->A->(A)hypermap`);
69 ("face_walkup", `:(A)hypermap->A->(A)hypermap`);
70 ("node_walkup", `:(A)hypermap->A->(A)hypermap`);
71 ("edge_walkup", `:(A)hypermap->A->(A)hypermap`);
72 ("shift", `:(A)hypermap->(A)hypermap`);
73 ("is_face_degenerate", `:(A)hypermap->A->bool`);
74 ("is_node_degenerate", `:(A)hypermap->A->bool`);
75 ("is_edge_degenerate", `:(A)hypermap->A->bool`);
76 ("isolated_dart", `:(A)hypermap->A->bool`);
77 ("is_inj_contour", `:(A)hypermap->(num->A)->num->bool`);
78 ("face_contour", `:(A)hypermap->A->num->A`);
79 ("node_contour", `:(A)hypermap->A->num->A`);
80 ("is_contour", `:(A)hypermap->(num->A)->num->bool`);
81 ("one_step_contour", `:(A)hypermap->A->A->bool`);
82 ("face_path", `:(A)hypermap->A->num->A`);
83 ("node_path", `:(A)hypermap->A->num->A`);
84 ("edge_path", `:(A)hypermap->A->num->A`);
85 ("connected_hypermap", `:(A)hypermap->bool`);
86 ("dart_nondegenerate", `:(A)hypermap->A->bool`);
87 ("dart_degenerate", `:(A)hypermap->A->bool`);
88 ("simple_hypermap", `:(A)hypermap->bool`);
89 ("planar_hypermap", `:(A)hypermap->bool`);
90 ("plain_hypermap", `:(A)hypermap->bool`);
91 ("number_of_components", `:(A)hypermap->num`);
92 ("number_of_faces", `:(A)hypermap->num`);
93 ("number_of_nodes", `:(A)hypermap->num`);
94 ("number_of_edges", `:(A)hypermap->num`);
95 ("set_of_components", `:(A)hypermap->(A->bool)->bool`);
96 ("set_part_components", `:(A)hypermap->(A->bool)->(A->bool)->bool`);
97 ("set_components", `:(A)hypermap->(A->bool)->(A->bool)->bool`);
98 ("face_set", `:(A)hypermap->(A->bool)->bool`);
99 ("node_set", `:(A)hypermap->(A->bool)->bool`);
100 ("edge_set", `:(A)hypermap->(A->bool)->bool`);
101 ("number_of_orbits", `:(A->bool)->(A->A)->num`);
102 ("set_of_orbits", `:(A->bool)->(A->A)->(A->bool)->bool`);
103 ("comb_component", `:(A)hypermap->A->A->bool`);
104 ("is_in_component", `:(A)hypermap->A->A->bool`);
105 ("is_path", `:(A)hypermap->(num->A)->num->bool`);
106 ("go_one_step", `:(A)hypermap->A->A->bool`);
107 ("face", `:(A)hypermap->A->A->bool`);
108 ("node", `:(A)hypermap->A->A->bool`);
109 ("edge", `:(A)hypermap->A->A->bool`); ("face_map", `:(A)hypermap->A->A`);
110 ("node_map", `:(A)hypermap->A->A`); ("edge_map", `:(A)hypermap->A->A`);
111 ("dart", `:(A)hypermap->A->bool`);
112 ("tuple_hypermap", `:(A)hypermap->(A->bool)#(A->A)#(A->A)#(A->A)`);
113 ("hypermap", `:(A->bool)#(A->A)#(A->A)#(A->A)->(A)hypermap`);
114 ("orbit_map", `:(A->A)->A->A->bool`); ("POWER", `:(A->A)->num->A->A`);
115 ("integer_point", `:(real^3->bool)->real^3->bool`);
116 ("map1", `:real^3->real^3->bool`);
117 ("close_hinhcau", `:real^3->real->real^3->bool`);
118 ("set_of_ccube", `:(real^3->bool)->(real^3->bool)->bool`);
119 ("ccube", `:real^3->real^3->bool`);
120 ("vector_to_pair", `:real^3->real#real#real`);
121 ("int_interval", `:real->real->real->bool`);
122 ("map0", `:real^3->real^3->bool`);
123 ("union_of_int_cube", `:real^3->real->real^3->bool`);
124 ("int_ball", `:real^3->real->real^3->bool`);
125 ("union_of_cube", `:real^3->real->real^3->bool`);
126 ("set_of_cube", `:(real^3->bool)->(real^3->bool)->bool`);
127 ("hinhcau", `:real^3->real->real^3->bool`);
128 ("cube", `:real^3->real^3->bool`);
129 ("sol", `:(real^3->bool)->real^3->real`);
130 ("volume_prop_fix", `:((real^3->bool)->real)->bool`);
131 ("eventually_radial_norm", `:real^A->(real^A->bool)->bool`);
132 ("radial_norm", `:real->real^A->(real^A->bool)->bool`);
133 ("parallel", `:real^N->real^N->bool`); ("unknown", `:bool`);
134 ("arg_diff", `:real^2->real^2->real`); ("pl_angle", `:real^2->real`);
135 ("polar_cycle_on", `:(real^2->real^2)->(real^2->bool)->bool`);
136 ("polar_le", `:real^2->real^2->bool`);
137 ("polar_lt", `:real^2->real^2->bool`); ("tri_itv", `:real->bool`);
138 ("real_itv", `:real->real->real->bool`);
139 ("sinV", `:real^A->real^A->real`); ("cosV", `:real^A->real^A->real`);
140 ("atan2_temp", `:real#real->real`);
142 `:real->real->real->real->real->real->real->real->real->real`);
143 ("quadratic_root_plus", `:real#real#real->real`);
144 ("abc_of_quadratic", `:(real->real)->real#real#real`);
146 `:real->real->real->real->real->real->real->real->real->real->real`);
147 ("muy_v", `:real^N->real^N->real^N->real^N->real^N->real->real`);
148 ("muy_delta", `:real->real->real->real->real->real->real`);
149 ("det_vec3", `:real^3->real^3->real^3->real`);
151 `:real^3->real^3->real^3->real^3->real->real->real->real->real->A->bool`);
152 ("coplanar_alt", `:(real^A->bool)->bool`);
154 `:real->real->real->real->real->real->real->real->real->real->real`);
155 ("delta_x14", `:real->real->real->real->real->real->real`);
156 ("delta_x13", `:real->real->real->real->real->real->real`);
157 ("delta_x12", `:real->real->real->real->real->real->real`);
158 ("coef3", `:real^N->real^N->real^N->real^N->real`);
159 ("coef2", `:real^N->real^N->real^N->real^N->real`);
160 ("coef1", `:real^N->real^N->real^N->real^N->real`);
161 ("c_coef", `:real->real->real->real->real->real`);
162 ("b_coef", `:real->real->real->real->real->real`);
163 ("cm3_ups_x", `:real^3->real^3->real^3->real`);
164 ("plane_3p", `:real^3->real^3->real^3->real^3->bool`);
165 ("delta_x34", `:real->real->real->real->real->real->real`);
166 ("plane_norm", `:(real^A->bool)->bool`);
167 ("ups_x_pow2", `:real->real->real->real`);
168 ("max_real3", `:real->real->real->real`);
169 ("max_real", `:real->real->real`);
170 ("eta_v", `:real^N->real^N->real^N->real`);
171 ("delta", `:real->real->real->real->real->real->real`);
172 ("chi", `:real->real->real->real->real->real->real`);
173 ("rho_ij", `:real->real->real->real->real->real->real`);
175 `:real->real->real->real->real->real->real->real->real->real->real`);
176 ("min_dist", `:real^3->(real^3->bool)->bool`);
177 ("e_plane", `:real^N->real^N->real^N->bool`);
178 ("near2t0", `:real^A->(real^A->bool)->real^A->bool`);
179 ("near", `:real^N->real->(real^N->bool)->real^N->bool`);
180 ("VC_INFI", `:(real^3->bool)->real^3->bool`);
181 ("VC", `:real^3->(real^3->bool)->real^3->bool`);
182 ("lambda_y", `:real^3->(real^3->bool)->real^3->bool`);
183 ("lambda_x", `:real^3->(real^3->bool)->real^3->bool`);
184 ("VC_INFI_trg", `:(real^3->bool)->real^3->bool`);
185 ("VC_trg", `:real^3->(real^3->bool)->real^3->bool`);
186 ("unobstructed", `:real^3->real^3->(real^3->bool)->bool`);
187 ("obstruct", `:real^3->real^3->(real^3->bool)->bool`);
188 ("conv", `:(real^A->bool)->real^A->bool`);
189 ("obstructed", `:real^3->real^3->(real^3->bool)->bool`);
190 ("barrier", `:(real^3->bool)->(real^3->bool)->bool`);
191 ("Q_SYS", `:(real^3->bool)->(real^3->bool)->bool`);
192 ("anchor_points", `:real^3->real^3->(real^3->bool)->real^3->bool`);
193 ("anchor", `:real^3->real^3->real^3->(real^3->bool)->bool`);
194 ("isolated_pai", `:(real^3->bool)->(real^3->bool)->(real^3->bool)->bool`);
195 ("isolated_qua", `:(real^3->bool)->(real^3->bool)->bool`);
197 `:real^3->real^3->real^3->real^3->real^3->(real^3->bool)->bool`);
199 `:real^3->real^3->real^3->real^3->real^3->(real^3->bool)->bool`);
201 `:real^3->real^3->real^3->real^3->real^3->(real^3->bool)->bool`);
203 `:real^3->real^3->real^3->real^3->real^3->real^3->(real^3->bool)->bool`);
204 ("strict_qua2", `:(real^3->bool)->(real^3->bool)->(real^3->bool)->bool`);
205 ("strict_qua", `:(real^3->bool)->(real^3->bool)->bool`);
206 ("diagonal", `:real^3->real^3->(real^3->bool)->(real^3->bool)->bool`);
207 ("quarter", `:(real^3->bool)->(real^3->bool)->bool`);
208 ("quasi_reg_tet", `:(real^3->bool)->(real^3->bool)->bool`);
209 ("simplex", `:(real^3->bool)->(real^3->bool)->bool`);
210 ("quasi_tri", `:(real^3->bool)->(real^3->bool)->bool`); ("t0", `:real`);
211 ("voro2", `:real^3->(real^3->bool)->real^3->bool`);
212 ("voronoi2", `:real^3->(real^3->bool)->real^3->bool`);
213 ("d3", `:real^3->real^3->real`);
214 ("centered_pac", `:(real^3->bool)->real^3->bool`);
215 ("center_pac", `:(real^3->bool)->real^3->bool`);
216 ("packing_trg", `:(real^3->bool)->bool`);
217 ("border", `:(real^A->bool)->real^A->bool`);
218 ("conv_trg", `:(real^A->bool)->real^A->bool`);
219 ("conv0_2", `:(real^A->bool)->real^A->bool`);
220 ("voronoi_trg", `:real^A->(real^A->bool)->real^A->bool`);
221 ("ineq", `:(real#real#real)list->bool->bool`);
222 ("abc_param", `:real^A->real^A->real^A->B->real#real#B`);
224 `:real^3->real^3->real^3->real^3->real->real->real->real^3`);
225 ("ortho0", `:real^A->real^A->real^A->real^A->real^A->bool`);
226 ("rcone_lt", `:real^A->real^A->real->real^A->bool`);
227 ("eventually_radial", `:real^A->(real^A->bool)->bool`);
228 ("radial", `:real->real^A->(real^A->bool)->bool`);
229 ("null_equiv", `:(real^3->bool)#(real^3->bool)->bool`);
230 ("packing", `:(real^3->bool)->bool`);
231 ("azim_cycle", `:(real^3->bool)->real^3->real^3->real^3->real^3`);
232 ("projection", `:real^A->real^A->real^A`);
233 ("cyclic_set", `:(real^A->bool)->real^A->real^A->bool`);
234 ("polar_cycle", `:(real#real->bool)->real#real->real#real`);
235 ("cyclic_order", `:real#real->real#real->real#real->bool`);
236 ("radius", `:real#real->real`);
237 ("directed_angle", `:real#real->real#real->real`);
238 ("beta", `:real->real->real`);
239 ("euler_p", `:real^A->real^A->real^A->real^A->real`);
241 `:real^A->real^A->real^A->real^A->real#real#real#real#real#real`);
243 `:real^A->real^A->real^A->real^A->real#real#real#real#real#real`);
244 ("orientation", `:(real^A->bool)->real^A->(real->bool)->bool`);
245 ("radV", `:(real^A->bool)->real`);
246 ("circumcenter", `:(real^A->bool)->real^A`);
247 ("bis_lt", `:real^A->real^A->real^A->bool`);
248 ("bis_le", `:real^A->real^A->real^A->bool`);
249 ("bis", `:real^A->real^A->real^A->bool`);
250 ("open_half_space", `:(real^A->bool)->bool`);
251 ("closed_half_space", `:(real^A->bool)->bool`);
252 ("open_half_plane", `:(real^A->bool)->bool`);
253 ("closed_half_plane", `:(real^A->bool)->bool`);
254 ("line", `:(real^A->bool)->bool`);
255 ("voronoi_le", `:real^A->(real^A->bool)->real^A->bool`);
256 ("voronoi", `:real^A->(real^A->bool)->real^A->bool`);
257 ("aff", `:(real^A->bool)->real^A->bool`);
258 ("rad2_x", `:real->real->real->real->real->real->real`);
259 ("dihR", `:real->real->real->real`); ("solR", `:real->real->real->real`);
260 ("volR", `:real->real->real->real`);
261 ("arclength", `:real->real->real->real`);
262 ("vol_x", `:real->real->real->real->real->real->real`);
263 ("tauq", `:real->real->real->real->real->real->real->real->real->real`);
264 ("taum", `:real->real->real->real->real->real->real`);
265 ("lnazim", `:real->real->real->real->real->real->real`);
266 ("rhazim", `:real->real->real->real->real->real->real`);
267 ("rho", `:real->real`); ("ly", `:real->real`); ("const1", `:real`);
268 ("interp", `:real->real->real->real->real->real`);
269 ("sol_y", `:real->real->real->real->real->real->real`);
270 ("sol_x", `:real->real->real->real->real->real->real`);
271 ("dih3_x", `:real->real->real->real->real->real->real`);
272 ("dih2_x", `:real->real->real->real->real->real->real`);
273 ("dih3_y", `:real->real->real->real->real->real->real`);
274 ("dih2_y", `:real->real->real->real->real->real->real`);
275 ("dih_y", `:real->real->real->real->real->real->real`);
276 ("dih_x", `:real->real->real->real->real->real->real`);
277 ("chi_x", `:real->real->real->real->real->real->real`);
278 ("rho_x", `:real->real->real->real->real->real->real`);
279 ("eta_y", `:real->real->real->real`);
280 ("eta_x", `:real->real->real->real`);
281 ("ups_x", `:real->real->real->real`);
282 ("delta_x6", `:real->real->real->real->real->real->real`);
283 ("delta_x4", `:real->real->real->real->real->real->real`);
284 ("delta_y", `:real->real->real->real->real->real->real`);
285 ("pi_rt18", `:real`); ("sqrt2", `:real`); ("sqrt8", `:real`);
286 ("atn2", `:real#real->real`); ("SDIFF", `:(A->bool)->(A->bool)->A->bool`);
287 ("vol_ball_wedge", `:real^3->real^3->real^3->real^3->real->real`);
288 ("vol_rect", `:real^A->real^B->real`);
289 ("vol_conv", `:real^A->real^A->real^A->real^A->real`);
290 ("vol_conic_cap_wedge",
291 `:real^3->real^3->real^3->real^3->real->real->real`);
292 ("vol_frustt_wedge", `:real^3->real^3->real^3->real^3->real->real->real`);
293 ("vol_solid_triangle", `:real^A->real^A->real^A->real^A->real->real`);
294 ("primitive", `:(real^3->bool)->bool`);
295 ("circular_cone", `:(real^3->bool)->bool`);
296 ("c_cone", `:real^3#real^3#real->real^3->bool`);
297 ("sphere", `:(real^3->bool)->bool`);
298 ("rect", `:real^3->real^3->real^3->bool`);
299 ("solid_triangle", `:real^A->(real^A->bool)->real->real^A->bool`);
300 ("cone0", `:real^A->(real^A->bool)->real^A->bool`);
301 ("cone", `:real^A->(real^A->bool)->real^A->bool`);
302 ("dihV", `:real^A->real^A->real^A->real^A->real`);
303 ("opposite", `:real^N->real^N->(real^N->bool)->bool`);
304 ("wedge", `:real^3->real^3->real^3->real^3->real^3->bool`);
305 ("azim", `:real^3->real^3->real^3->real^3->real`);
306 ("arcV", `:real^A->real^A->real^A->real`);
307 ("orthonormal", `:real^3->real^3->real^3->bool`);
308 ("conic_cap", `:real^A->real^A->real->real->real^A->bool`);
309 ("ellipsoid", `:real^3->real->real^3->bool`);
310 ("normball", `:real^A->real->real^A->bool`);
311 ("scale", `:real^3->real^3->real^3`);
312 ("frustt", `:real^A->real^A->real->real->real^A->bool`);
313 ("frustum", `:real^N->real^N->real->real->real->real^N->bool`);
314 ("rcone_eq", `:real^A->real^A->real->real^A->bool`);
315 ("rcone_ge", `:real^A->real^A->real->real^A->bool`);
316 ("rcone_gt", `:real^A->real^A->real->real^A->bool`);
317 ("rconesgn", `:(real->real->bool)->real^A->real^A->real->real^A->bool`);
318 ("delta_x", `:real->real->real->real->real->real->real`);
319 ("conv0", `:(real^A->bool)->real^A->bool`);
320 ("aff_le", `:(real^A->bool)->(real^A->bool)->real^A->bool`);
321 ("aff_lt", `:(real^A->bool)->(real^A->bool)->real^A->bool`);
322 ("aff_ge", `:(real^A->bool)->(real^A->bool)->real^A->bool`);
323 ("aff_gt", `:(real^A->bool)->(real^A->bool)->real^A->bool`);
324 ("sgn_le", `:real->bool`); ("sgn_lt", `:real->bool`);
325 ("sgn_ge", `:real->bool`); ("sgn_gt", `:real->bool`);
326 ("affsign", `:(real->bool)->(real^A->bool)->(real^A->bool)->real^A->bool`);
327 ("lin_combo", `:(real^N->bool)->(real^N->real)->real^N`);
328 ("pad2d3d", `:real^2->real^3`); ("plane", `:(real^A->bool)->bool`);
329 ("slice", `:num->real->(real^A->bool)->real^B->bool`);
330 ("pushin", `:num->B->B^A->B^C`); ("dropout", `:num->real^N->real^M`);
331 ("real_measure", `:(real->bool)->real`);
332 ("real_measurable", `:(real->bool)->bool`);
333 ("has_real_measure", `:(real->bool)->real->bool`);
334 ("absolutely_real_integrable_on", `:(real->real)->(real->bool)->bool`);
335 ("real_negligible", `:(real->bool)->bool`);
336 ("real_integral", `:(real->bool)->(real->real)->real`);
337 ("real_integrable_on", `:(real->real)->(real->bool)->bool`);
338 ("has_real_integral", `:(real->real)->real->(real->bool)->bool`);
339 ("closed_real_interval", `:(real#real)list->real->bool`);
340 ("open_real_interval", `:real#real->real->bool`);
341 ("is_realinterval", `:(real->bool)->bool`);
342 ("real_differentiable_on", `:(real->real)->(real->bool)->bool`);
343 ("higher_real_derivative", `:num->(real->real)->real->real`);
344 ("real_derivative", `:(real->real)->real->real`);
345 ("real_differentiable", `:(real->real)->(real)net->bool`);
346 ("has_real_derivative", `:(real->real)->real->(real)net->bool`);
347 ("real_continuous_on", `:(real->real)->(real->bool)->bool`);
348 ("real_continuous", `:(A->real)->(A)net->bool`);
349 ("at_neginfinity", `:(real)net`); ("at_posinfinity", `:(real)net`);
350 ("atreal", `:real->(real)net`);
351 ("real_summable", `:(num->bool)->(num->real)->bool`);
352 ("real_infsum", `:(num->bool)->(num->real)->real`);
353 ("real_sums", `:(num->real)->real->(num->bool)->bool`);
354 ("--->", `:(A->real)->real->(A)net->bool`);
355 ("real_compact", `:(real->bool)->bool`);
356 ("real_bounded", `:(real->bool)->bool`);
357 ("euclideanreal", `:(real)topology`);
358 ("real_closed", `:(real->bool)->bool`);
359 ("real_open", `:(real->bool)->bool`);
360 ("measure", `:(real^A->bool)->real`);
361 ("measurable", `:(real^A->bool)->bool`);
362 ("has_measure", `:(real^A->bool)->real->bool`);
363 ("*_c", `:(A->bool)->(B->bool)->A#B->bool`);
364 ("+_c", `:(A->bool)->(B->bool)->A+B->bool`);
365 ("ordinal", `:(A#A->bool)->bool`);
366 ("linseg", `:(A#A->bool)->A->A#A->bool`);
367 ("inseg", `:(A#A->bool)->(A#A->bool)->bool`);
368 ("woset", `:(A#A->bool)->bool`);
369 ("chain", `:(A#A->bool)->(A->bool)->bool`);
370 ("poset", `:(A#A->bool)->bool`); ("fl", `:(A#A->bool)->A->bool`);
371 ("less", `:(A#A->bool)->A#A->bool`);
372 ("angle", `:real^A#real^A#real^A->real`);
373 ("vector_angle", `:real^A->real^A->real`); ("acs", `:real->real`);
374 ("asn", `:real->real`); ("cacs", `:real^2->real^2`);
375 ("casn", `:real^2->real^2`); ("atn", `:real->real`);
376 ("catn", `:real^2->real^2`); ("unwinding", `:real^2->real^2`);
377 ("cpow", `:real^2->real^2->real^2`); ("clog", `:real^2->real^2`);
378 ("tan", `:real->real`); ("ctan", `:real^2->real^2`);
379 ("rotate2d", `:real->real^2->real^2`); ("Arg", `:real^2->real`);
380 ("pi", `:real`); ("log", `:real->real`); ("cos", `:real->real`);
381 ("sin", `:real->real`); ("exp", `:real->real`);
382 ("csin", `:real^2->real^2`); ("ccos", `:real^2->real^2`);
383 ("cexp", `:real^2->real^2`);
384 ("analytic_on", `:(real^2->real^2)->(real^2->bool)->bool`);
385 ("holomorphic_on", `:(real^2->real^2)->(real^2->bool)->bool`);
386 ("higher_complex_derivative", `:num->(real^2->real^2)->real^2->real^2`);
387 ("complex_derivative", `:(real^2->real^2)->real^2->real^2`);
388 ("complex_differentiable", `:(real^2->real^2)->(real^2)net->bool`);
389 ("has_complex_derivative", `:(real^2->real^2)->real^2->(real^2)net->bool`);
390 ("cproduct", `:(A->bool)->(A->real^2)->real^2`);
391 ("real", `:real^2->bool`); ("csqrt", `:real^2->real^2`);
392 ("cnj", `:real^2->real^2`); ("complex_pow", `:real^2->num->real^2`);
393 ("complex_div", `:real^2->real^2->real^2`);
394 ("complex_inv", `:real^2->real^2`);
395 ("complex_mul", `:real^2->real^2->real^2`); ("ii", `:real^2`);
396 ("Cx", `:real->real^2`); ("complex", `:real#real->real^2`);
397 ("Im", `:real^2->real`); ("Re", `:real^2->real`);
398 ("absolutely_integrable_on", `:(real^B->real^A)->(real^B->bool)->bool`);
399 ("negligible", `:(real^A->bool)->bool`);
400 ("indicator", `:(real^M->bool)->real^M->real^1`);
402 `:(real^N->bool)->((real^N->bool)->bool)->num#real->bool`);
403 ("lifted", `:(A->A->B)->(A)option->(A)option->(B)option`);
404 ("operative", `:(A->A->A)->((real^N->bool)->A)->bool`);
405 ("integral", `:(real^A->bool)->(real^A->real^B)->real^B`);
406 ("integrable_on", `:(real^B->real^A)->(real^B->bool)->bool`);
407 ("has_integral", `:(real^B->real^A)->real^A->(real^B->bool)->bool`);
408 ("has_integral_compact_interval",
409 `:(real^B->real^A)->real^A->(real^B->bool)->bool`);
410 ("fine", `:(A->B->bool)->(A#(B->bool)->bool)->bool`);
411 ("tagged_division_of",
412 `:(real^A#(real^A->bool)->bool)->(real^A->bool)->bool`);
413 ("tagged_partial_division_of",
414 `:(real^A#(real^A->bool)->bool)->(real^A->bool)->bool`);
415 ("division_of", `:((real^A->bool)->bool)->(real^A->bool)->bool`);
416 ("gauge", `:(real^A->real^A->bool)->bool`);
417 ("content", `:(real^M->bool)->real`);
418 ("interval_lowerbound", `:(real^M->bool)->real^M`);
419 ("interval_upperbound", `:(real^M->bool)->real^M`);
420 ("vector_derivative", `:(real^1->real^N)->(real^1)net->real^N`);
421 ("has_vector_derivative", `:(real^1->real^A)->real^A->(real^1)net->bool`);
422 ("jacobian", `:(real^A->real^B)->(real^A)net->real^A^B`);
423 ("frechet_derivative", `:(real^A->real^B)->(real^A)net->real^A->real^B`);
424 ("differentiable_on", `:(real^B->real^A)->(real^B->bool)->bool`);
425 ("differentiable", `:(real^B->real^A)->(real^B)net->bool`);
427 `:(real^B->real^A)->(real^B->real^A)->(real^B)net->bool`);
428 ("interval_bij", `:real^N#real^N->real^N#real^N->real^N->real^N`);
429 ("retract_of", `:(real^A->bool)->(real^A->bool)->bool`);
430 ("retraction", `:(real^N->bool)#(real^N->bool)->(real^N->real^N)->bool`);
431 ("reduced", `:((num->num)->num->num)->num->(num->num)->num`);
432 ("ksimplex", `:num->num->((num->num)->bool)->bool`);
433 ("kle", `:num->(num->num)->(num->num)->bool`);
434 ("path_connected", `:(real^A->bool)->bool`);
435 ("path_component", `:(real^A->bool)->real^A->real^A->bool`);
436 ("linepath", `:real^A#real^A->real^1->real^A`);
437 ("shiftpath", `:real^1->(real^1->real^N)->real^1->real^N`);
438 ("arc", `:(real^1->real^N)->bool`);
439 ("simple_path", `:(real^1->real^N)->bool`);
440 ("++", `:(real^1->A)->(real^1->A)->real^1->A`);
441 ("reversepath", `:(real^1->real^N)->real^1->real^N`);
442 ("path_image", `:(real^1->real^N)->real^N->bool`);
443 ("pathfinish", `:(real^1->real^N)->real^N`);
444 ("pathstart", `:(real^1->real^N)->real^N`);
445 ("path", `:(real^1->real^N)->bool`);
446 ("extreme_point_of", `:real^A->(real^A->bool)->bool`);
447 ("face_of", `:(real^A->bool)->(real^A->bool)->bool`);
448 ("relative_interior", `:(real^A->bool)->real^A->bool`);
449 ("starlike", `:(real^A->bool)->bool`);
451 `:(real^N->bool)->(real^N->real)->real^(N,1)finite_sum->bool`);
452 ("convex_on", `:(real^A->real)->(real^A->bool)->bool`);
453 ("coplanar", `:(real^A->bool)->bool`);
454 ("affine_dependent", `:(real^N->bool)->bool`);
455 ("conic", `:(real^A->bool)->bool`); ("convex", `:(real^A->bool)->bool`);
456 ("affine", `:(real^A->bool)->bool`);
457 ("closest_point", `:(real^A->bool)->real^A->real^A`);
458 ("from", `:num->num->bool`);
459 ("summable", `:(num->bool)->(num->real^A)->bool`);
460 ("infsum", `:(num->bool)->(num->real^A)->real^A`);
461 ("sums", `:(num->real^A)->real^A->(num->bool)->bool`);
462 ("homeomorphic", `:(real^A->bool)->(real^B->bool)->bool`);
464 `:(real^B->bool)#(real^A->bool)->(real^B->real^A)#(real^A->real^B)->bool`);
465 ("open_segment", `:real^A#real^A->real^A->bool`);
466 ("closed_segment", `:(real^A#real^A)list->real^A->bool`);
467 ("is_interval", `:(real^N->bool)->bool`);
468 ("closed_interval", `:(real^N#real^N)list->real^N->bool`);
469 ("open_interval", `:real^N#real^N->real^N->bool`);
470 ("diameter", `:(real^A->bool)->real`);
471 ("connected_component", `:(real^A->bool)->real^A->real^A->bool`);
472 ("uniformly_continuous_on", `:(real^B->real^A)->(real^B->bool)->bool`);
473 ("continuous_on", `:(real^B->real^A)->(real^B->bool)->bool`);
474 ("continuous", `:(B->real^A)->(B)net->bool`);
475 ("complete", `:(real^N->bool)->bool`); ("cauchy", `:(num->real^N)->bool`);
476 ("compact", `:(real^N->bool)->bool`);
477 ("bounded", `:(real^N->bool)->bool`); ("netlimit", `:(A)net->A`);
478 ("lim", `:(A)net->(A->real^B)->real^B`);
479 ("-->", `:(B->real^A)->real^A->(B)net->bool`);
480 ("eventually", `:(A->bool)->(A)net->bool`);
481 ("trivial_limit", `:(A)net->bool`);
482 ("in_direction", `:real^A->real^A->(real^A)net`);
483 ("within", `:(A)net->(A->bool)->(A)net`); ("sequentially", `:(num)net`);
484 ("at_infinity", `:(real^A)net`); ("at", `:real^A->(real^A)net`);
485 ("netord", `:(A)net->A->A->bool`); ("mk_net", `:(A->A->bool)->(A)net`);
486 ("frontier", `:(real^A->bool)->real^A->bool`);
487 ("closure", `:(real^A->bool)->real^A->bool`);
488 ("interior", `:(real^A->bool)->real^A->bool`);
489 ("limit_point_of", `:real^A->(real^A->bool)->bool`);
490 ("connected", `:(real^A->bool)->bool`);
491 ("cball", `:real^A#real->real^A->bool`);
492 ("ball", `:real^A#real->real^A->bool`);
493 ("euclidean", `:(real^A)topology`); ("closed", `:(real^N->bool)->bool`);
494 ("open", `:(real^A->bool)->bool`);
495 ("subtopology", `:(A)topology->(A->bool)->(A)topology`);
496 ("closed_in", `:(A)topology->(A->bool)->bool`);
497 ("topspace", `:(A)topology->A->bool`);
498 ("open_in", `:(A)topology->(A->bool)->bool`);
499 ("topology", `:((A->bool)->bool)->(A)topology`);
500 ("istopology", `:((A->bool)->bool)->bool`);
501 ("ITER", `:num->(A->A)->A->A`); ("frac", `:real->real`);
502 ("floor", `:real->real`); ("integer", `:real->bool`);
503 ("cross", `:real^3->real^3->real^3`);
504 ("rotoinversion_matrix", `:real^A^A->bool`);
505 ("rotation_matrix", `:real^A^A->bool`);
506 ("orthogonal_matrix", `:real^N^N->bool`);
507 ("orthogonal_transformation", `:(real^N->real^N)->bool`);
508 ("det", `:real^N^N->real`); ("trace", `:real^N^N->real`);
509 ("product", `:(A->bool)->(A->real)->real`); ("sign", `:(A->A)->real`);
510 ("evenperm", `:(A->A)->bool`); ("permutation", `:(A->A)->bool`);
511 ("swapseq", `:num->(A->A)->bool`); ("swap", `:A#A->A->A`);
512 ("inverse", `:(B->A)->A->B`); ("permutes", `:(A->A)->(A->bool)->bool`);
513 ("midpoint", `:real^A#real^A->real^A`);
514 ("between", `:real^A->real^A#real^A->bool`);
515 ("collinear", `:(real^A->bool)->bool`); ("infnorm", `:real^N->real`);
516 ("rank", `:real^M^N->num`); ("columnvector", `:real^N->real^1^N`);
517 ("rowvector", `:real^N->real^N^1`); ("dim", `:(real^A->bool)->num`);
518 ("independent", `:(real^A->bool)->bool`);
519 ("dependent", `:(real^A->bool)->bool`);
520 ("span", `:(real^A->bool)->real^A->bool`);
521 ("subspace", `:(real^A->bool)->bool`); ("drop", `:real^1->real`);
522 ("lift", `:real->real^1`); ("onorm", `:(real^M->real^N)->real`);
523 ("matrix", `:(real^M->real^N)->real^M^N`);
524 ("matrix_inv", `:real^N^M->real^M^N`); ("invertible", `:real^N^M->bool`);
525 ("columns", `:real^N^M->real^M->bool`);
526 ("rows", `:real^N^M->real^N->bool`); ("column", `:num->real^N^M->real^M`);
527 ("row", `:num->real^N^M->real^N`); ("transp", `:real^N^M->real^M^N`);
528 ("mat", `:num->real^N^M`);
529 ("vector_matrix_mul", `:real^M->real^N^M->real^N`);
530 ("matrix_vector_mul", `:real^N^M->real^N->real^M`);
531 ("matrix_mul", `:real^N^M->real^P^N->real^P^M`);
532 ("matrix_sub", `:real^N^M->real^N^M->real^N^M`);
533 ("matrix_add", `:real^N^M->real^N^M->real^N^M`);
534 ("matrix_neg", `:real^N^M->real^N^M`);
535 ("adjoint", `:(real^M->real^N)->real^N->real^M`);
536 ("bilinear", `:(real^A->real^B->real^C)->bool`);
537 ("linear", `:(real^M->real^N)->bool`);
538 ("orthogonal", `:real^A->real^A->bool`); ("basis", `:num->real^A`);
539 ("vsum", `:(A->bool)->(A->real^N)->real^N`);
540 ("distance", `:real^A#real^A->real`); ("vector_norm", `:real^A->real`);
541 ("dot", `:real^N->real^N->real`); ("vec", `:num->real^N`);
542 ("%", `:real->real^N->real^N`); ("vector_neg", `:real^N->real^N`);
543 ("vector_sub", `:real^N->real^N->real^N`);
544 ("vector_add", `:real^N->real^N->real^N`); ("sqrt", `:real->real`);
545 ("hull", `:((A->bool)->bool)->(A->bool)->A->bool`);
546 ("inf", `:(real->bool)->real`); ("sup", `:(real->bool)->real`);
548 `:(A->A->bool)->((A->C)->B->bool)->(B->A)->((A->C)->B->C)->bool`);
550 `:(A->A->bool)->((A->B)->P->bool)->(P->A)->((A->B)->P->B)->bool`);
552 `:(B->A->bool)->((B->C)->D->bool)->(D->A)->((B->C)->D->E)->bool`);
553 ("CASEWISE", `:((A->C)#(B->A->D))list->B->C->D`);
554 ("vector", `:(A)list->A^N`);
555 ("dest_auto_define_finite_type_3", `:3->num`);
556 ("mk_auto_define_finite_type_3", `:num->3`);
557 ("dest_auto_define_finite_type_2", `:2->num`);
558 ("mk_auto_define_finite_type_2", `:num->2`);
559 ("sndcart", `:A^(M,N)finite_sum->A^N`);
560 ("fstcart", `:A^(M,N)finite_sum->A^M`);
561 ("pastecart", `:A^M->A^N->A^(M,N)finite_sum`);
562 ("dest_finite_sum", `:(A,B)finite_sum->num`);
563 ("mk_finite_sum", `:num->(A,B)finite_sum`); ("lambda", `:(num->A)->A^B`);
564 ("$", `:B^A->num->B`); ("dest_cart", `:A^B->(B)finite_image->A`);
565 ("mk_cart", `:((B)finite_image->A)->A^B`);
566 ("dest_finite_image", `:(A)finite_image->num`);
567 ("finite_index", `:num->(A)finite_image`);
568 ("dimindex", `:(A->bool)->num`); ("sum", `:(A->bool)->(A->real)->real`);
569 ("nsum", `:(A->bool)->(A->num)->num`);
570 ("iterate", `:(B->B->B)->(A->bool)->(A->B)->B`);
571 ("support", `:(B->B->B)->(A->B)->(A->bool)->A->bool`);
572 ("monoidal", `:(A->A->A)->bool`); ("neutral", `:(A->A->A)->A`);
573 ("..", `:num->num->num->bool`); ("COUNTABLE", `:(A->bool)->bool`);
574 (">_c", `:(A->bool)->(B->bool)->bool`);
575 (">=_c", `:(A->bool)->(B->bool)->bool`);
576 ("=_c", `:(A->bool)->(B->bool)->bool`);
577 ("<_c", `:(A->bool)->(B->bool)->bool`);
578 ("<=_c", `:(A->bool)->(B->bool)->bool`);
579 ("PAIRWISE", `:(A->A->bool)->(A)list->bool`);
580 ("pairwise", `:(A->A->bool)->(A->bool)->bool`);
581 ("list_of_set", `:(A->bool)->(A)list`);
582 ("set_of_list", `:(A)list->A->bool`);
583 ("CROSS", `:(A->bool)->(B->bool)->A#B->bool`);
584 ("HAS_SIZE", `:(A->bool)->num->bool`); ("CARD", `:(A->bool)->num`);
585 ("ITSET", `:(A->B->B)->(A->bool)->B->B`);
586 ("FINREC", `:(A->B->B)->B->(A->bool)->B->num->bool`);
587 ("REST", `:(A->bool)->A->bool`); ("CHOICE", `:(A->bool)->A`);
588 ("BIJ", `:(A->B)->(A->bool)->(B->bool)->bool`);
589 ("SURJ", `:(A->B)->(A->bool)->(B->bool)->bool`);
590 ("INJ", `:(A->B)->(A->bool)->(B->bool)->bool`);
591 ("IMAGE", `:(A->B)->(A->bool)->B->bool`);
592 ("INFINITE", `:(A->bool)->bool`); ("FINITE", `:(A->bool)->bool`);
593 ("SING", `:(A->bool)->bool`); ("DISJOINT", `:(A->bool)->(A->bool)->bool`);
594 ("PSUBSET", `:(A->bool)->(A->bool)->bool`);
595 ("SUBSET", `:(A->bool)->(A->bool)->bool`);
596 ("DELETE", `:(A->bool)->A->A->bool`);
597 ("DIFF", `:(A->bool)->(A->bool)->A->bool`);
598 ("INTERS", `:((A->bool)->bool)->A->bool`);
599 ("INTER", `:(A->bool)->(A->bool)->A->bool`);
600 ("UNIONS", `:((A->bool)->bool)->A->bool`);
601 ("UNION", `:(A->bool)->(A->bool)->A->bool`); ("UNIV", `:A->bool`);
602 ("INSERT", `:A->(A->bool)->A->bool`); ("EMPTY", `:A->bool`);
603 ("SETSPEC", `:A->bool->A->bool`); ("GSPEC", `:(A->bool)->A->bool`);
604 ("IN", `:A->(A->bool)->bool`); ("num_gcd", `:num#num->num`);
605 ("num_coprime", `:num#num->bool`); ("num_mod", `:num->num->num->bool`);
606 ("num_divides", `:num->num->bool`); ("num_of_int", `:int->num`);
607 ("int_gcd", `:int#int->int`); ("int_coprime", `:int#int->bool`);
608 ("int_mod", `:int->int->int->bool`); ("int_divides", `:int->int->bool`);
609 ("real_mod", `:real->real->real->bool`);
610 ("==", `:A->A->(A->A->bool)->bool`); ("rem", `:int->int->int`);
611 ("div", `:int->int->int`); ("int_pow", `:int->num->int`);
612 ("int_min", `:int->int->int`); ("int_max", `:int->int->int`);
613 ("int_abs", `:int->int`); ("int_mul", `:int->int->int`);
614 ("int_sub", `:int->int->int`); ("int_add", `:int->int->int`);
615 ("int_neg", `:int->int`); ("int_of_num", `:num->int`);
616 ("int_gt", `:int->int->bool`); ("int_ge", `:int->int->bool`);
617 ("int_lt", `:int->int->bool`); ("int_le", `:int->int->bool`);
618 ("real_of_int", `:int->real`); ("int_of_real", `:real->int`);
619 ("is_int", `:real->bool`); ("DECIMAL", `:num->num->real`);
620 ("real_min", `:real->real->real`); ("real_max", `:real->real->real`);
621 ("real_div", `:real->real->real`); ("real_pow", `:real->num->real`);
622 ("real_abs", `:real->real`); ("real_gt", `:real->real->bool`);
623 ("real_ge", `:real->real->bool`); ("real_lt", `:real->real->bool`);
624 ("real_sub", `:real->real->real`); ("real_inv", `:real->real`);
625 ("real_le", `:real->real->bool`); ("real_mul", `:real->real->real`);
626 ("real_add", `:real->real->real`); ("real_neg", `:real->real`);
627 ("real_of_num", `:num->real`); ("dest_real", `:real->hreal#hreal->bool`);
628 ("mk_real", `:(hreal#hreal->bool)->real`);
629 ("treal_eq", `:hreal#hreal->hreal#hreal->bool`);
630 ("treal_inv", `:hreal#hreal->hreal#hreal`);
631 ("treal_le", `:hreal#hreal->hreal#hreal->bool`);
632 ("treal_mul", `:hreal#hreal->hreal#hreal->hreal#hreal`);
633 ("treal_add", `:hreal#hreal->hreal#hreal->hreal#hreal`);
634 ("treal_neg", `:hreal#hreal->hreal#hreal`);
635 ("treal_of_num", `:num->hreal#hreal`); ("hreal_inv", `:hreal->hreal`);
636 ("hreal_le", `:hreal->hreal->bool`);
637 ("hreal_mul", `:hreal->hreal->hreal`);
638 ("hreal_add", `:hreal->hreal->hreal`); ("hreal_of_num", `:num->hreal`);
639 ("dest_hreal", `:hreal->nadd->bool`);
640 ("mk_hreal", `:(nadd->bool)->hreal`); ("nadd_inv", `:nadd->nadd`);
641 ("nadd_rinv", `:nadd->num->num`); ("nadd_mul", `:nadd->nadd->nadd`);
642 ("nadd_add", `:nadd->nadd->nadd`); ("nadd_le", `:nadd->nadd->bool`);
643 ("nadd_of_num", `:num->nadd`); ("nadd_eq", `:nadd->nadd->bool`);
644 ("dest_nadd", `:nadd->num->num`); ("mk_nadd", `:(num->num)->nadd`);
645 ("is_nadd", `:(num->num)->bool`); ("dist", `:num#num->num`);
646 ("ASCII", `:bool->bool->bool->bool->bool->bool->bool->bool->char`);
647 ("_16756", `:bool->bool->bool->bool->bool->bool->bool->bool->char`);
648 ("_dest_char", `:char->(bool#bool#bool#bool#bool#bool#bool#bool)recspace`);
649 ("_mk_char", `:(bool#bool#bool#bool#bool#bool#bool#bool)recspace->char`);
650 ("ZIP", `:(A)list->(B)list->(A#B)list`);
651 ("ITLIST2", `:(A->B->C->C)->(A)list->(B)list->C->C`);
652 ("ASSOC", `:A->(A#B)list->B`); ("FILTER", `:(A->bool)->(A)list->(A)list`);
653 ("EL", `:num->(A)list->A`);
654 ("MAP2", `:(A->B->C)->(A)list->(B)list->(C)list`);
655 ("ALL2", `:(A->B->bool)->(A)list->(B)list->bool`);
656 ("MEM", `:A->(A)list->bool`); ("ITLIST", `:(A->B->B)->(A)list->B->B`);
657 ("EX", `:(A->bool)->(A)list->bool`); ("ALL", `:(A->bool)->(A)list->bool`);
658 ("NULL", `:(A)list->bool`); ("REPLICATE", `:num->A->(A)list`);
659 ("LAST", `:(A)list->A`); ("MAP", `:(A->B)->(A)list->(B)list`);
660 ("LENGTH", `:(A)list->num`); ("REVERSE", `:(A)list->(A)list`);
661 ("APPEND", `:(A)list->(A)list->(A)list`); ("TL", `:(A)list->(A)list`);
662 ("HD", `:(A)list->A`); ("ISO", `:(A->B)->(B->A)->bool`);
663 ("CONS", `:A->(A)list->(A)list`); ("NIL", `:(A)list`);
664 ("_dest_list", `:(A)list->(A)recspace`);
665 ("_mk_list", `:(A)recspace->(A)list`); ("SOME", `:A->(A)option`);
666 ("NONE", `:(A)option`); ("_dest_option", `:(A)option->(A)recspace`);
667 ("_mk_option", `:(A)recspace->(A)option`); ("OUTR", `:A+B->B`);
668 ("OUTL", `:A+B->A`); ("INR", `:B->A+B`); ("INL", `:A->A+B`);
669 ("_dest_sum", `:A+B->(A#B)recspace`); ("_mk_sum", `:(A#B)recspace->A+B`);
670 ("FNIL", `:num->A`); ("FCONS", `:A->(num->A)->num->A`);
671 ("CONSTR", `:num->A->(num->(A)recspace)->(A)recspace`);
672 ("BOTTOM", `:(A)recspace`); ("_dest_rec", `:(A)recspace->num->A->bool`);
673 ("_mk_rec", `:(num->A->bool)->(A)recspace`);
674 ("ZRECSPACE", `:(num->A->bool)->bool`); ("ZBOT", `:num->A->bool`);
675 ("ZCONSTR", `:num->A->(num->num->A->bool)->num->A->bool`);
676 ("INJP", `:(num->A->bool)->(num->A->bool)->num->A->bool`);
677 ("INJF", `:(num->num->A->bool)->num->A->bool`);
678 ("INJA", `:A->num->A->bool`); ("INJN", `:num->num->A->bool`);
679 ("NUMRIGHT", `:num->num`); ("NUMLEFT", `:num->bool`);
680 ("NUMSUM", `:bool->num->num`); ("NUMSND", `:num->num`);
681 ("NUMFST", `:num->num`); ("NUMPAIR", `:num->num->num`);
682 ("MEASURE", `:(A->num)->A->A->bool`); ("WF", `:(A->A->bool)->bool`);
683 ("minimal", `:(num->bool)->num`); ("MIN", `:num->num->num`);
684 ("MAX", `:num->num->num`); ("MOD", `:num->num->num`);
685 ("DIV", `:num->num->num`); ("FACT", `:num->num`); ("-", `:num->num->num`);
686 ("ODD", `:num->bool`); ("EVEN", `:num->bool`); (">", `:num->num->bool`);
687 (">=", `:num->num->bool`); ("<", `:num->num->bool`);
688 ("<=", `:num->num->bool`); ("EXP", `:num->num->num`);
689 ("*", `:num->num->num`); ("BIT1", `:num->num`); ("BIT0", `:num->num`);
690 ("+", `:num->num->num`); ("PRE", `:num->num`); ("NUMERAL", `:num->num`);
691 ("SUC", `:num->num`); ("_0", `:num`); ("dest_num", `:num->ind`);
692 ("mk_num", `:ind->num`); ("NUM_REP", `:ind->bool`); ("IND_0", `:ind`);
693 ("IND_SUC", `:ind->ind`); ("ONTO", `:(A->B)->bool`);
694 ("ONE_ONE", `:(A->B)->bool`); ("PASSOC", `:((A#B)#C->D)->A#B#C->D`);
695 ("UNCURRY", `:(A->B->C)->A#B->C`); ("CURRY", `:(A#B->C)->A->B->C`);
696 ("SND", `:A#B->B`); ("FST", `:A#B->A`); (",", `:A->B->A#B`);
697 ("REP_prod", `:A#B->A->B->bool`); ("ABS_prod", `:(A->B->bool)->A#B`);
698 ("mk_pair", `:A->B->A->B->bool`); ("_FUNCTION", `:(A->B->bool)->A->B`);
699 ("_MATCH", `:A->(A->B->bool)->B`);
700 ("_GUARDED_PATTERN", `:bool->bool->bool->bool`);
701 ("_UNGUARDED_PATTERN", `:bool->bool->bool`);
702 ("_SEQPATTERN", `:(A->B->bool)->(A->B->bool)->A->B->bool`);
703 ("GEQ", `:A->A->bool`); ("GABS", `:(A->bool)->A`); ("LET_END", `:A->A`);
704 ("LET", `:(A->B)->A->B`); ("one", `:1`); ("one_REP", `:1->bool`);
705 ("one_ABS", `:bool->1`); ("I", `:A->A`); ("o", `:(B->C)->(A->B)->A->C`);
706 ("COND", `:bool->A->A->A`); ("@", `:(A->bool)->A`);
707 ("_FALSITY_", `:bool`); ("?!", `:(A->bool)->bool`); ("~", `:bool->bool`);
708 ("F", `:bool`); ("\\/", `:bool->bool->bool`); ("?", `:(A->bool)->bool`);
709 ("!", `:(A->bool)->bool`); ("==>", `:bool->bool->bool`);
710 ("/\\", `:bool->bool->bool`); ("T", `:bool`); ("=", `:A->A->bool`)];;
712 let the_loaded_files =
713 ["flyspeck_utility.hl"; "update_database_310.ml"; "hypermap.hl"; "vol1.hl";
714 "trigonometry.hl"; "database2194fe.ml"; "flyspeck_utility.hl"; "trig2.hl";
715 "trig1.hl"; "ineqdata3q1h.hl"; "ineq.hl"; "enclosed_def.hl";
716 "quadratic_root_plus_def.hl"; "abc_of_quadratic_def.hl"; "muR_def.hl";
717 "collect_geom.hl"; "cayleyR_def.hl"; "affprops.hl"; "AFF_SGN_TAC.hl";
718 "geomdetail.hl"; "snapshot.hl"; "snapshot.hl"; "snapshot.hl";
719 "snapshot.hl"; "snapshot.hl"; "sphere.hl"; "prove_by_refinement.hl";
720 "update_database_310.ml"; "database3be71a.ml"; "snapshot.hl";
721 "print-types.ml"; "flyspeck.ml"; "wlog_examples.ml"; "wlog.ml"; "real.ml";
722 "measure.ml"; "card.ml"; "wo.ml"; "geom.ml"; "transc.ml"; "canal.ml";
723 "complex.ml"; "integration.ml"; "analysis.ml"; "dimension.ml";
724 "convex.ml"; "topology.ml"; "iter.ml"; "floor.ml"; "cross.ml";
725 "determinants.ml"; "products.ml"; "permutations.ml"; "vectors.ml";
726 "misc.ml"; "database.ml"; "help.ml"; "define.ml"; "cart.ml"; "iter.ml";
727 "sets.ml"; "int.ml"; "calc_rat.ml"; "real.ml"; "realarith.ml";
728 "calc_int.ml"; "realax.ml"; "list.ml"; "ind-types.ml"; "grobner.ml";
729 "normalizer.ml"; "calc_num.ml"; "wf.ml"; "arith.ml"; "num.ml"; "pair.ml";
730 "recursion.ml"; "quot.ml"; "meson.ml"; "canon.ml"; "trivia.ml";
731 "class.ml"; "ind-defs.ml"; "theorems.ml"; "simp.ml"; "itab.ml";
732 "tactics.ml"; "drule.ml"; "bool.ml"; "equal.ml"; "printer.ml";
733 "parser.ml"; "preterm.ml"; "nets.ml"; "basics.ml"; "fusion.ml"; "lib.ml";
736 let the_types = [("loop", 1); ("hypermap", 1); ("net", 1); ("topology", 1); ("3", 0);
737 ("2", 0); ("finite_sum", 2); ("cart", 2); ("finite_image", 1); ("int", 0);
738 ("real", 0); ("hreal", 0); ("nadd", 0); ("char", 0); ("list", 1);
739 ("option", 1); ("sum", 2); ("recspace", 1); ("num", 0); ("ind", 0);
740 ("prod", 2); ("1", 0); ("bool", 0); ("fun", 2)];;
742 let the_overload_skeletons = Snapshot_v220_7_31_2009.the_overload_skeletons;;