- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / relocation / lexs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma
index 7fd35071acaea51d259b3f7f828de5ab4ee4970a..e99ea0393c3c992e54cf8c82c91ddeec2c4869ab 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma
@@ -14,7 +14,7 @@
 
 include "ground_2/relocation/rtmap_sle.ma".
 include "basic_2/notation/relations/relationstar_5.ma".
-include "basic_2/grammar/lenv.ma".
+include "basic_2/syntax/lenv.ma".
 
 (* GENERIC ENTRYWISE EXTENSION OF CONTEXT-SENSITIVE REALTIONS FOR TERMS *****)
 
@@ -32,12 +32,14 @@ inductive lexs (RN,RP:relation3 lenv term term): rtmap → relation lenv ≝
 interpretation "generic entrywise extension (local environment)"
    'RelationStar RN RP f L1 L2 = (lexs RN RP f L1 L2).
 
-definition lexs_confluent: relation6 (relation3 lenv term term)
-                                     (relation3 lenv term term) … ≝
-                           λR1,R2,RN1,RP1,RN2,RP2.
-                           ∀f,L0,T0,T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 →
-                           ∀L1. L0 ⦻*[RN1, RP1, f] L1 → ∀L2. L0 ⦻*[RN2, RP2, f] L2 →
-                           ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
+definition R_pw_confluent2_lexs: relation3 lenv term term → relation3 lenv term term →
+                                 relation3 lenv term term → relation3 lenv term term →
+                                 relation3 lenv term term → relation3 lenv term term →
+                                 relation3 rtmap lenv term ≝
+                                 λR1,R2,RN1,RP1,RN2,RP2,f,L0,T0.
+                                 ∀T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 →
+                                 ∀L1. L0 ⦻*[RN1, RP1, f] L1 → ∀L2. L0 ⦻*[RN2, RP2, f] L2 →
+                                 ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
 
 definition lexs_transitive: relation5 (relation3 lenv term term)
                                       (relation3 lenv term term) … ≝
@@ -181,6 +183,22 @@ lemma lexs_refl: ∀RN,RP,f.
 #L #I #V #IH * * /2 width=1 by lexs_next, lexs_push/
 qed.
 
+lemma lexs_pair_repl: ∀RN,RP,f,I,L1,L2,V1,V2.
+                      L1.ⓑ{I}V1 ⦻*[RN, RP, f] L2.ⓑ{I}V2 →
+                      ∀W1,W2. RN L1 W1 W2 → RP L1 W1 W2 →
+                      L1.ⓑ{I}W1 ⦻*[RN, RP, f] L2.ⓑ{I}W2.
+#RN #RP #f #I #L1 #L2 #V1 #V2 #HL12 #W1 #W2 #HN #HP
+elim (lexs_fwd_pair … HL12) -HL12 /2 width=1 by lexs_inv_tl/
+qed-.
+
+lemma lexs_co: ∀RN1,RP1,RN2,RP2.
+               (∀L1,T1,T2. RN1 L1 T1 T2 → RN2 L1 T1 T2) →
+               (∀L1,T1,T2. RP1 L1 T1 T2 → RP2 L1 T1 T2) →
+               ∀f,L1,L2. L1 ⦻*[RN1, RP1, f] L2 → L1 ⦻*[RN2, RP2, f] L2.
+#RN1 #RP1 #RN2 #RP2 #HRN #HRP #f #L1 #L2 #H elim H -f -L1 -L2
+/3 width=1 by lexs_atom, lexs_next, lexs_push/
+qed-.
+
 lemma sle_lexs_trans: ∀RN,RP. (∀L,T1,T2. RN L T1 T2 → RP L T1 T2) →
                       ∀f2,L1,L2. L1 ⦻*[RN, RP, f2] L2 →
                       ∀f1. f1 ⊆ f2 → L1 ⦻*[RN, RP, f1] L2.
@@ -206,11 +224,3 @@ lemma sle_lexs_conf: ∀RN,RP. (∀L,T1,T2. RP L T1 T2 → RN L T1 T2) →
   #g2 #H #H2 destruct /3 width=5 by lexs_next/
 ]
 qed-.
-
-lemma lexs_co: ∀RN1,RP1,RN2,RP2.
-               (∀L1,T1,T2. RN1 L1 T1 T2 → RN2 L1 T1 T2) →
-               (∀L1,T1,T2. RP1 L1 T1 T2 → RP2 L1 T1 T2) →
-               ∀f,L1,L2. L1 ⦻*[RN1, RP1, f] L2 → L1 ⦻*[RN2, RP2, f] L2.
-#RN1 #RP1 #RN2 #RP2 #HRN #HRP #f #L1 #L2 #H elim H -f -L1 -L2
-/3 width=1 by lexs_atom, lexs_next, lexs_push/
-qed-.