X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fi_static%2Ftc_lfxs_lex.ma;h=918191c8fb75cdee0d978583681996ab4cc5c064;hb=5c186c72f508da0849058afeecc6877cd9ed6303;hp=dbcf5fe44a6c105529a49bffbf74284eb87b7c2b;hpb=775106f04b47236bf47e4321d745ec360ab4ebb4;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_lex.ma b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_lex.ma
index dbcf5fe44..918191c8f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_lex.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/i_static/tc_lfxs_lex.ma
@@ -12,11 +12,9 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/syntax/ext2_tc.ma".
-include "basic_2/relocation/lexs_tc.ma".
-include "basic_2/relocation/lex.ma".
+include "basic_2/relocation/lex_tc.ma".
 include "basic_2/static/lfeq_fqup.ma".
-include "basic_2/static/lfeq_lfeq.ma".
+include "basic_2/static/lfeq_fsle.ma".
 include "basic_2/i_static/tc_lfxs_fqup.ma".
 
 (* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
@@ -24,25 +22,27 @@ include "basic_2/i_static/tc_lfxs_fqup.ma".
 (* Properties with generic extension of a context sensitive relation ********)
 
 lemma tc_lfxs_lex: ∀R. c_reflexive … R →
-                   ∀L1,L2,T. L1 ⪤[LTC … R] L2 → L1 ⪤**[R, T] L2.
+                   ∀L1,L2,T. L1 ⪤[CTC … R] L2 → L1 ⪤**[R, T] L2.
 #R #HR #L1 #L2 #T *
 /5 width=7 by tc_lfxs_tc, lexs_inv_tc_dx, lexs_co, ext2_inv_tc, ext2_refl/
 qed.
 
 lemma tc_lfxs_lex_lfeq: ∀R. c_reflexive … R →
-                        ∀L1,L. L1 ⪤[LTC … R] L → ∀L2,T. L ≡[T] L2 →
+                        ∀L1,L. L1 ⪤[CTC … R] L → ∀L2,T. L ≡[T] L2 →
                         L1 ⪤**[R, T] L2.
 /3 width=3 by tc_lfxs_lex, tc_lfxs_step_dx, lfeq_fwd_lfxs/ qed.
 
 (* Inversion lemmas with generic extension of a context sensitive relation **)
 
+(* Note: s_rs_transitive_lex_inv_isid could be invoked in the last auto but makes it too slow *)
 lemma tc_lfxs_inv_lex_lfeq: ∀R. c_reflexive … R →
-                            lexs_frees_confluent (cext2 R) cfull →
-                            s_rs_transitive_isid cfull (cext2 R) →
+                            lfxs_fsge_compatible R →
+                            s_rs_transitive … R (λ_.lex R) →
                             lfeq_transitive R →
                             ∀L1,L2,T. L1 ⪤**[R, T] L2 →
-                            ∃∃L. L1 ⪤[LTC … R] L & L ≡[T] L2.
+                            ∃∃L. L1 ⪤[CTC … R] L & L ≡[T] L2.
 #R #H1R #H2R #H3R #H4R #L1 #L2 #T #H
+lapply (s_rs_transitive_lex_inv_isid … H3R) -H3R #H3R
 @(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
@@ -50,9 +50,9 @@ lemma tc_lfxs_inv_lex_lfeq: ∀R. c_reflexive … R →
   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
+  elim (frees_lexs_conf … Hf1 … H) // -H2R -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_co ?? cfull (CTC … (cext2 R)) … HL1) -HL1 /2 width=1 by ext2_inv_tc/ #HL1
   /8 width=11 by lexs_inv_tc_dx, lexs_tc_dx, lexs_co, ext2_tc, ext2_refl, step, ex2_intro/ (**) (* full auto too slow *)
 ]
 qed-.