- ground_2: rtmap: disjointness relation

[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
index 53782a58dca04b261b8e92865ce60abe3fb76609..64e38fc4892e6a85f12c2113e417babdb751489c 100644 (file)
--- 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
@@ -12,56 +12,35 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/static/lfeq.ma".
+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".
 
-(*
-axiom cext2_inv_LTC: ∀R,L,I1,I2. cext2 (LTC … R) L I1 I2 → LTC … (cext2 R) L I1 I2.
-
-#R #L #I1 #I2 * -I1 -I2
-[ /2 width=1 by ext2_unit, inj/
-| #I #V1 #V2 #HV12 
-*)
-
-  
-(*
-lemma pippo: ∀RN,RP. (∀L. reflexive … (RP L)) →
-             ∀f,L1,L2. L1 ⪤*[LTC … RN, RP, f] L2 →
-             TC … (lexs RN RP f) L1 L2.
-#RN #RP #HRP #f #L1 #L2 #H elim H -f -L1 -L2
-[ /2 width=1 by lexs_atom, inj/ ]
-#f #I1 #I2 #L1 #L2 #HL12 #HI12 #IH 
-[ @step [3: 
-*)
-
-(*
-axiom lexs_frees_confluent_LTC_sn: ∀RN,RP. lexs_frees_confluent RN RP →
-                                   lexs_frees_confluent (LTC … RN) RP.
-
-#RN #RP #HR #f1 #L1 #T #Hf1 #L2 #H  
-*)
 (* ITERATED EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ***)
 
-lemma pippo: ∀R. (∀L. reflexive … (R L)) →
-             (lexs_frees_confluent (cext2 R) cfull) →
-             ∀L1,L2,T. L1 ⪤**[R, T] L2 →
-             ∃∃L. L1 ⪤*[LTC … R, T] L & L ≡[T] L2.
-#R #H1R #H2R #L1 #L2 #T #H
+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=5 by lfxs_refl, inj, ex2_intro/
-| #L0 #L2 #_ #HL02 * #L * #f1 #Hf1 #HL1 #HL0
-  lapply (lexs_co ??? cfull … (cext2_inv_LTC R) … HL1) -HL1 // #HL1
-  lapply (lfeq_lfxs_trans … HL0 … HL02) -L0 #HL2
-  elim (lexs_frees_confluent_LTC_sn … H2R … Hf1 … HL1) #f2 #Hf2 #Hf21
-  lapply (lfxs_inv_frees … HL2 … Hf2) -HL2 #HL2
-  elim (lexs_sle_split … ceq_ext … HL2 … Hf21) -HL2
-  [ #L0 #HL0 #HL02
-  |*: /2 width=1 by ext2_refl/
-  ]
-  lapply (sle_lexs_trans … HL0 … Hf21) -Hf21 // #H
-  elim (H2R … Hf2 … H) -H #f0 #Hf0 #Hf02
-  lapply (sle_lexs_trans … HL02 … Hf02) -f2 // #HL02
-  @(ex2_intro … L0)
-  [ @(ex2_intro … Hf1)
-  | @(ex2_intro … HL02) //
+[ /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-.