- equivalene of tc_lfxs and lex + lfeq proved

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / i_static / tc_lfxs_lfeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_lfeq.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_lfeq.ma
deleted file mode 100644 (file)
index 64e38fc..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_lfeq.ma
+++ /dev/null
@@ -1,46 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/syntax/ext2_tc.ma".
-include "basic_2/relocation/lexs_tc.ma".
-include "basic_2/relocation/lex.ma".
-include "basic_2/static/lfeq_fqup.ma".
-include "basic_2/static/lfxs_lfxs.ma".
-include "basic_2/i_static/tc_lfxs_fqup.ma".
-
-(* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
-
-lemma tc_lfxs_inv_lex_lfeq: ∀R. c_reflexive … R →
-                            (lexs_frees_confluent (cext2 R) cfull) →
-                            (∀f. 𝐈⦃f⦄ → s_rs_transitive … (cext2 R) (λ_.lexs cfull (cext2 R) f)) →
-                            ∀L1,L2,T. L1 ⪤**[R, T] L2 →
-                            ∃∃L. L1 ⪤[LTC … R] L & L ≡[T] L2.
-#R #H1R #H2R #H3R #L1 #L2 #T #H
-@(tc_lfxs_ind_sn … H1R … H) -H -L2
-[ /4 width=3 by lfeq_refl, lex_refl, inj, ex2_intro/
-| #L0 #L2 #_ #HL02 * #L * #f0 #Hf0 #HL1 #HL0
-  lapply (lfeq_lfxs_trans … HL0 … HL02) -L0 * #f1 #Hf1 #HL2
-  elim (lexs_sdj_split … ceq_ext … HL2 f0 ?) -HL2
-  [ #L0 #HL0 #HL02 |*: /2 width=1 by ext2_refl, sdj_isid_dx/ ]
-  lapply (lexs_sdj … HL0 f1 ?) /2 width=1 by sdj_isid_sn/ #H
-  elim (H2R … Hf1 … H) -H #f2 #Hf2 #Hf21
-  lapply (sle_lexs_trans … HL02 … Hf21) -f1 // #HL02
-  lapply (lexs_co ?? cfull (LTC … (cext2 R)) … HL1) -HL1 /2 width=1 by ext2_inv_tc/ #HL1  
-  lapply (lexs_inv_tc_dx … HL1) -HL1 /2 width=1 by ext2_refl/ #HL1
-  lapply (step ????? HL1 … HL0) -L #HL10
-  lapply (lexs_tc_dx … H3R … HL10) -HL10 // #HL10
-  lapply (lexs_co … cfull (cext2 (LTC … R)) … HL10) -HL10 /2 width=1 by ext2_tc/ #HL10
-  /3 width=5 by ex2_intro/
-]
-qed-.