1 (* Copyright (C) 2002, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
7 * HELM is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation; either version 2
10 * of the License, or (at your option) any later version.
12 * HELM is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with HELM; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
26 open HelmLibraryObjects
28 let debug_print = fun _ -> ()
30 let rec injection_tac ~term =
31 let injection_tac ~term status =
32 let (proof, goal) = status in
34 let module U = UriManager in
35 let module P = PrimitiveTactics in
36 let module T = Tacticals in
37 let _,metasenv,_,_ = proof in
38 let _,context,_ = CicUtil.lookup_meta goal metasenv in
39 let termty,_ = (* TASSI: FIXME *)
40 CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
41 ProofEngineTypes.apply_tactic
43 (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
44 when (U.eq equri Logic.eq_URI) -> (
46 (C.MutInd (turi,typeno,exp_named_subst))
47 | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> (
49 ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
50 (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
51 when (uri1 = uri2) && (typeno1 = typeno2) &&
52 (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
53 (* raise (ProofEngineTypes.Fail "Injection: nothing to do") ; *) T.id_tac
54 | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
55 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
56 when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
57 let rec traverse_list i l1 l2 =
60 | hd1::tl1,hd2::tl2 ->
62 ~start:(injection1_tac ~i ~term)
63 ~continuation:(traverse_list (i+1) tl1 tl2)
64 | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???") ; T.id_tac
65 in traverse_list 1 applist1 applist2
66 | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
67 (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
68 | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
69 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
70 | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
71 (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
72 | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
73 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
74 when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
75 (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality but a discriminable one") ; *) T.id_tac
76 | _ -> (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality") ; *) T.id_tac
78 | _ -> raise (ProofEngineTypes.Fail "Injection: not a projectable equality")
80 | _ -> raise (ProofEngineTypes.Fail "Injection: not an equation")
83 ProofEngineTypes.mk_tactic (injection_tac ~term)
85 and injection1_tac ~term ~i =
86 let injection1_tac ~term ~i status =
87 let (proof, goal) = status in
88 (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma differiscono (o potrebbero differire?) nell'i-esimo parametro del costruttore *)
90 let module S = CicSubstitution in
91 let module U = UriManager in
92 let module P = PrimitiveTactics in
93 let module T = Tacticals in
94 let _,metasenv,_,_ = proof in
95 let _,context,_ = CicUtil.lookup_meta goal metasenv in
96 let termty,_ = (* TASSI: FIXME *)
97 CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
98 match termty with (* an equality *)
99 (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
100 when (U.eq equri Logic.eq_URI) -> (
101 match tty with (* some inductive type *)
102 (C.MutInd (turi,typeno,exp_named_subst))
103 | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
104 let t1',t2',consno = (* sono i due sottotermini che differiscono *)
106 ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
107 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
108 when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) -> (* controllo ridondante *)
109 (List.nth applist1 (i-1)),(List.nth applist2 (i-1)),consno2
113 CicTypeChecker.type_of_aux' metasenv context t1'
114 CicUniv.empty_ugraph in
116 match fst(CicEnvironment.get_obj
117 CicUniv.empty_ugraph turi ) with
118 C.InductiveDefinition (ind_type_list,_,nr_ind_params_dx,_) ->
119 let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
120 let i_constr_id,_ = List.nth constructor_list (consno - 1) in
122 (function (id,cty) ->
123 let reduced_cty = CicReduction.whd context cty in
126 C.Prod (_,_,target) when (k <= nr_ind_params_dx) ->
128 | C.Prod (binder,source,target) when (k > nr_ind_params_dx) ->
132 | C.Anonymous -> C.Name "y"
134 C.Lambda (binder',source,(aux target (k+1)))
136 let nr_param_constr = k - 1 - nr_ind_params_dx in
137 if (id = i_constr_id)
138 then C.Rel (nr_param_constr - i + 1)
139 else S.lift (nr_param_constr + 1) t1' (* + 1 per liftare anche il lambda agguinto esternamente al case *)
143 | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
145 ProofEngineTypes.apply_tactic
147 ~start:(P.cut_tac (C.Appl [(C.MutInd (equri,0,[])) ; tty' ; t1' ; t2']))
150 ~start:(injection_tac ~term:(C.Rel 1))
151 ~continuation:T.id_tac (* !!! qui devo anche fare clear di term tranne al primo passaggio *)
154 ~start:(ProofEngineTypes.mk_tactic
156 let (proof, goal) = status in
157 let _,metasenv,_,_ = proof in
158 let _,context,gty = CicUtil.lookup_meta goal metasenv in
161 (C.Appl (C.MutInd (_,_,_)::arglist)) ->
163 | _ -> raise (ProofEngineTypes.Fail "Injection: goal after cut is not correct")
165 ProofEngineTypes.apply_tactic
166 (ReductionTactics.change_tac
167 ~pattern:(ProofEngineTypes.conclusion_pattern (Some new_t1'))
187 (EqualityTactics.rewrite_simpl_tac
188 ~direction:`LeftToRight
189 ~pattern:(ProofEngineTypes.conclusion_pattern None)
191 ~continuation:EqualityTactics.reflexivity_tac
195 | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
197 | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
199 ProofEngineTypes.mk_tactic (injection1_tac ~term ~i)
204 exception TwoDifferentSubtermsFound of int
206 (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
209 let discriminate'_tac ~term =
210 let discriminate'_tac ~term status =
211 let (proof, goal) = status in
212 let module C = Cic in
213 let module U = UriManager in
214 let module P = PrimitiveTactics in
215 let module T = Tacticals in
216 let _,metasenv,_,_ = proof in
217 let _,context,_ = CicUtil.lookup_meta goal metasenv in
219 CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
221 (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
222 when (U.eq equri Logic.eq_URI) -> (
224 (C.MutInd (turi,typeno,exp_named_subst))
225 | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
227 let consno2 = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
229 let rec traverse t1 t2 =
231 ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
232 (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
233 when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
235 | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
236 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
237 when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
238 let rec traverse_list l1 l2 =
241 | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2
242 | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")
243 in traverse_list applist1 applist2
245 | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
246 (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
247 | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
248 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
249 | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
250 (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
251 | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
252 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
253 when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
254 raise (TwoDifferentSubtermsFound consno2)
255 | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
257 with (TwoDifferentSubtermsFound consno2) -> consno2
260 then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
264 (* a list of "True" except for the element in position consno2 which is "False" *)
265 match fst(CicEnvironment.get_obj
266 CicUniv.empty_ugraph turi) with
267 C.InductiveDefinition (ind_type_list,_,nr_ind_params,_) ->
268 let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
269 let false_constr_id,_ = List.nth constructor_list (consno2 - 1) in
271 (function (id,cty) ->
272 let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
275 C.Prod (_,_,target) when (k <= nr_ind_params) ->
277 | C.Prod (binder,source,target) when (k > nr_ind_params) ->
278 C.Lambda (binder,source,(aux target (k+1)))
280 if (id = false_constr_id)
281 then (C.MutInd(Logic.false_URI,0,[]))
282 else (C.MutInd(Logic.true_URI,0,[]))
286 | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
289 let (proof',goals') =
290 ProofEngineTypes.apply_tactic
291 (EliminationTactics.elim_type_tac
292 ~term:(C.MutInd(Logic.false_URI,0,[])))
297 let _,metasenv',_,_ = proof' in
298 let _,context',gty' =
299 CicUtil.lookup_meta goal' metasenv'
301 ProofEngineTypes.apply_tactic
304 (ReductionTactics.change_tac
305 ~pattern:(ProofEngineTypes.conclusion_pattern (Some gty'))
311 (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
322 (EqualityTactics.rewrite_simpl_tac
323 ~direction:`RightToLeft
324 ~pattern:(ProofEngineTypes.conclusion_pattern None)
326 ~continuation:(IntroductionTactics.constructor_tac ~n:1)
329 | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
331 | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
333 | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
335 ProofEngineTypes.mk_tactic (discriminate'_tac ~term)
338 let discriminate_tac ~term =
339 let discriminate_tac ~term status =
340 ProofEngineTypes.apply_tactic
342 ~start:(* (injection_tac ~term) *) Tacticals.id_tac
343 ~continuation:(discriminate'_tac ~term)) (* NOOO!!! non term ma una (qualunque) delle nuove hyp introdotte da inject *)
346 ProofEngineTypes.mk_tactic (discriminate_tac ~term)
351 let decide_equality_tac =
352 (* il goal e' un termine della forma t1=t2\/~t1=t2; la tattica decide se l'uguaglianza
353 e' vera o no e lo risolve *)
359 let compare_tac ~term = Tacticals.id_tac
361 (* term is in the form t1=t2; the tactic leaves two goals: in the first you have to *)
362 (* demonstrate the goal with the additional hyp that t1=t2, in the second the hyp is ~t1=t2 *)
363 let module C = Cic in
364 let module U = UriManager in
365 let module P = PrimitiveTactics in
366 let module T = Tacticals in
367 let _,metasenv,_,_ = proof in
368 let _,context,gty = CicUtil.lookup_meta goal metasenv in
369 let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
371 (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
373 let term' = (* (t1=t2)\/~(t1=t2) *)
375 (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ;
378 (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"), 1, [])) ;
380 C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
385 ~start:(P.cut_tac ~term:term')
387 T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
390 | (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
391 let term' = (* (t1=t2) \/ ~(t1=t2) *)
393 (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ;
396 (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind"), 1, [])) ;
398 C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
403 ~start:(P.cut_tac ~term:term')
405 T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
408 | _ -> raise (ProofEngineTypes.Fail "Compare: Not an equality")
414 (* DISCRIMINTATE SENZA INJECTION
416 exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int)
418 let discriminate_tac ~term status =
419 let module C = Cic in
420 let module U = UriManager in
421 let module P = PrimitiveTactics in
422 let module T = Tacticals in
423 let (proof, goal) = status in
424 let _,metasenv,_,_ = proof in
425 let _,context,_ = CicUtil.lookup_meta goal metasenv in
426 let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
428 (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
429 when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"))
430 or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> (
432 (C.MutInd (turi,typeno,exp_named_subst))
433 | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
435 let (t1',t2',consno2') = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
437 let rec traverse t1 t2 =
438 debug_print ("XXXX t1 " ^ CicPp.ppterm t1) ;
439 debug_print ("XXXX t2 " ^ CicPp.ppterm t2) ;
441 ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
442 (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
443 when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
445 | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
446 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
447 when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
448 let rec traverse_list l1 l2 =
451 | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2
452 | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")
453 in traverse_list applist1 applist2
455 | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
456 (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
457 | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
458 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
459 | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
460 (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
461 | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
462 (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
463 when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
464 raise (TwoDifferentSubtermsFound (t1,t2,consno2))
465 | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
467 with (TwoDifferentSubtermsFound (t1,t2,consno2)) -> (t1,t2,consno2)
469 debug_print ("XXXX consno2' " ^ (string_of_int consno2')) ;
471 then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
475 (* a list of "True" except for the element in position consno2' which is "False" *)
476 match fst(CicEnvironment.get_obj turi
477 CicUniv.empty_ugraph) with
478 C.InductiveDefinition (ind_type_list,_,nr_ind_params) ->
479 debug_print ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno)) ;
480 let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
481 debug_print ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2')) ;
482 let false_constr_id,_ = List.nth constructor_list (consno2' - 1) in
483 debug_print ("XXXX nth funzionano ") ;
485 (function (id,cty) ->
486 let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
489 C.Prod (_,_,target) when (k <= nr_ind_params) ->
491 | C.Prod (binder,source,target) when (k > nr_ind_params) ->
492 C.Lambda (binder,source,(aux target (k+1)))
494 if (id = false_constr_id)
495 then (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [])
496 else (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/True.ind") 0 [])
500 | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
503 let (proof',goals') =
504 EliminationTactics.elim_type_tac
505 ~term:(C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] )
510 let _,metasenv',_,_ = proof' in
511 let _,context',gty' =
512 CicUtil.lookup_meta goal' metasenv'
524 (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
533 debug_print ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])));
534 debug_print ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2'])) ;
535 debug_print ("XXXX equri: " ^ U.string_of_uri equri) ;
536 debug_print ("XXXX tty : " ^ CicPp.ppterm tty) ;
537 debug_print ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ;
538 debug_print ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
539 if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> tty then debug_print ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1')) ;
540 if (CicTypeChecker.type_of_aux' metasenv' context' t2') <> tty then debug_print ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
541 if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> (CicTypeChecker.type_of_aux' metasenv' context' t2')
542 then debug_print ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux'
543 metasenv' context' t1')) ; debug_print ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2')) ;
545 let termty' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t1 ~with_what:t1' ~where:termty in
546 let termty'' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t2 ~with_what:t2' ~where:termty' in
548 debug_print ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term));
550 ~start:(EqualityTactics.rewrite_back_simpl_tac ~term:term)
551 ~continuation:(IntroductionTactics.constructor_tac ~n:1)
554 | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
556 | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
558 | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")