renaming

[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 a589666960aa5f6e3171ddd2495c3808fb8c09ff..0ff659b1376689e45afb7fdca00469607a70a691 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lexs.ma
@@ -23,10 +23,10 @@ inductive lexs (RN,RP:relation3 lenv bind bind): rtmap → relation lenv ≝
 | lexs_atom: ∀f. lexs RN RP f (⋆) (⋆)
 | lexs_next: ∀f,I1,I2,L1,L2.
              lexs RN RP f L1 L2 → RN L1 I1 I2 →
-             lexs RN RP (⫯f) (L1.ⓘ{I1}) (L2.ⓘ{I2})
+             lexs RN RP (â\86\91f) (L1.ⓘ{I1}) (L2.ⓘ{I2})
 | lexs_push: ∀f,I1,I2,L1,L2.
              lexs RN RP f L1 L2 → RP L1 I1 I2 →
-             lexs RN RP (â\86\91f) (L1.ⓘ{I1}) (L2.ⓘ{I2})
+             lexs RN RP (⫯f) (L1.ⓘ{I1}) (L2.ⓘ{I2})
 .
 
 interpretation "generic entrywise extension (local environment)"
@@ -36,16 +36,18 @@ definition R_pw_confluent2_lexs: relation3 lenv bind bind → relation3 lenv bin
                                  relation3 lenv bind bind → relation3 lenv bind bind →
                                  relation3 lenv bind bind → relation3 lenv bind bind →
                                  relation3 rtmap lenv bind ≝
-                                 λR1,R2,RN1,RP1,RN2,RP2,f,L0,T0.
-                                 ∀T1. R1 L0 T0 T1 → ∀T2. R2 L0 T0 T2 →
+                                 λR1,R2,RN1,RP1,RN2,RP2,f,L0,I0.
+                                 ∀I1. R1 L0 I0 I1 → ∀I2. R2 L0 I0 I2 →
                                  ∀L1. L0 ⪤*[RN1, RP1, f] L1 → ∀L2. L0 ⪤*[RN2, RP2, f] L2 →
-                                 ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
+                                 ∃∃I. R2 L1 I1 I & R1 L2 I2 I.
 
-definition lexs_transitive: relation5 (relation3 lenv bind bind)
-                                      (relation3 lenv bind bind) … ≝
-                            λR1,R2,R3,RN,RP.
-                            ∀f,L1,T1,T. R1 L1 T1 T → ∀L2. L1 ⪤*[RN, RP, f] L2 →
-                            ∀T2. R2 L2 T T2 → R3 L1 T1 T2.
+definition lexs_transitive: relation3 lenv bind bind → relation3 lenv bind bind →
+                            relation3 lenv bind bind →
+                            relation3 lenv bind bind → relation3 lenv bind bind →
+                            relation3 rtmap lenv bind ≝
+                            λR1,R2,R3,RN,RP,f,L1,I1.
+                            ∀I. R1 L1 I1 I → ∀L2. L1 ⪤*[RN, RP, f] L2 →
+                            ∀I2. R2 L2 I I2 → R3 L1 I1 I2.
 
 (* Basic inversion lemmas ***************************************************)
 
@@ -58,7 +60,7 @@ qed-.
 lemma lexs_inv_atom1: ∀RN,RP,f,Y. ⋆ ⪤*[RN, RP, f] Y → Y = ⋆.
 /2 width=6 by lexs_inv_atom1_aux/ qed-.
 
-fact lexs_inv_next1_aux: â\88\80RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y â\86\92 â\88\80g,J1,K1. X = K1.â\93\98{J1} â\86\92 f = ⫯g →
+fact lexs_inv_next1_aux: â\88\80RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y â\86\92 â\88\80g,J1,K1. X = K1.â\93\98{J1} â\86\92 f = â\86\91g →
                          ∃∃J2,K2. K1 ⪤*[RN, RP, g] K2 & RN K1 J1 J2 & Y = K2.ⓘ{J2}.
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #g #J1 #K1 #H destruct
@@ -69,11 +71,11 @@ fact lexs_inv_next1_aux: ∀RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y → ∀g,J1,K1. X =
 qed-.
 
 (* Basic_2A1: includes lpx_sn_inv_pair1 *)
-lemma lexs_inv_next1: â\88\80RN,RP,g,J1,K1,Y. K1.â\93\98{J1} ⪤*[RN, RP, ⫯g] Y →
+lemma lexs_inv_next1: â\88\80RN,RP,g,J1,K1,Y. K1.â\93\98{J1} ⪤*[RN, RP, â\86\91g] Y →
                       ∃∃J2,K2. K1 ⪤*[RN, RP, g] K2 & RN K1 J1 J2 & Y = K2.ⓘ{J2}.
 /2 width=7 by lexs_inv_next1_aux/ qed-.
 
-fact lexs_inv_push1_aux: â\88\80RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y â\86\92 â\88\80g,J1,K1. X = K1.â\93\98{J1} â\86\92 f = â\86\91g →
+fact lexs_inv_push1_aux: â\88\80RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y â\86\92 â\88\80g,J1,K1. X = K1.â\93\98{J1} â\86\92 f = ⫯g →
                          ∃∃J2,K2. K1 ⪤*[RN, RP, g] K2 & RP K1 J1 J2 & Y = K2.ⓘ{J2}.
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #g #J1 #K1 #H destruct
@@ -83,7 +85,7 @@ fact lexs_inv_push1_aux: ∀RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y → ∀g,J1,K1. X =
 ]
 qed-.
 
-lemma lexs_inv_push1: â\88\80RN,RP,g,J1,K1,Y. K1.â\93\98{J1} ⪤*[RN, RP, â\86\91g] Y →
+lemma lexs_inv_push1: â\88\80RN,RP,g,J1,K1,Y. K1.â\93\98{J1} ⪤*[RN, RP, ⫯g] Y →
                       ∃∃J2,K2. K1 ⪤*[RN, RP, g] K2 & RP K1 J1 J2 & Y = K2.ⓘ{J2}.
 /2 width=7 by lexs_inv_push1_aux/ qed-.
 
@@ -96,7 +98,7 @@ qed-.
 lemma lexs_inv_atom2: ∀RN,RP,f,X. X ⪤*[RN, RP, f] ⋆ → X = ⋆.
 /2 width=6 by lexs_inv_atom2_aux/ qed-.
 
-fact lexs_inv_next2_aux: â\88\80RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y â\86\92 â\88\80g,J2,K2. Y = K2.â\93\98{J2} â\86\92 f = ⫯g →
+fact lexs_inv_next2_aux: â\88\80RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y â\86\92 â\88\80g,J2,K2. Y = K2.â\93\98{J2} â\86\92 f = â\86\91g →
                          ∃∃J1,K1. K1 ⪤*[RN, RP, g] K2 & RN K1 J1 J2 & X = K1.ⓘ{J1}.
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #g #J2 #K2 #H destruct
@@ -107,11 +109,11 @@ fact lexs_inv_next2_aux: ∀RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y → ∀g,J2,K2. Y =
 qed-.
 
 (* Basic_2A1: includes lpx_sn_inv_pair2 *)
-lemma lexs_inv_next2: â\88\80RN,RP,g,J2,X,K2. X ⪤*[RN, RP, ⫯g] K2.ⓘ{J2} →
+lemma lexs_inv_next2: â\88\80RN,RP,g,J2,X,K2. X ⪤*[RN, RP, â\86\91g] K2.ⓘ{J2} →
                       ∃∃J1,K1. K1 ⪤*[RN, RP, g] K2 & RN K1 J1 J2 & X = K1.ⓘ{J1}.
 /2 width=7 by lexs_inv_next2_aux/ qed-.
 
-fact lexs_inv_push2_aux: â\88\80RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y â\86\92 â\88\80g,J2,K2. Y = K2.â\93\98{J2} â\86\92 f = â\86\91g →
+fact lexs_inv_push2_aux: â\88\80RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y â\86\92 â\88\80g,J2,K2. Y = K2.â\93\98{J2} â\86\92 f = ⫯g →
                          ∃∃J1,K1. K1 ⪤*[RN, RP, g] K2 & RP K1 J1 J2 & X = K1.ⓘ{J1}.
 #RN #RP #f #X #Y * -f -X -Y
 [ #f #J2 #K2 #g #H destruct
@@ -121,20 +123,20 @@ fact lexs_inv_push2_aux: ∀RN,RP,f,X,Y. X ⪤*[RN, RP, f] Y → ∀g,J2,K2. Y =
 ]
 qed-.
 
-lemma lexs_inv_push2: â\88\80RN,RP,g,J2,X,K2. X ⪤*[RN, RP, â\86\91g] K2.ⓘ{J2} →
+lemma lexs_inv_push2: â\88\80RN,RP,g,J2,X,K2. X ⪤*[RN, RP, ⫯g] K2.ⓘ{J2} →
                       ∃∃J1,K1. K1 ⪤*[RN, RP, g] K2 & RP K1 J1 J2 & X = K1.ⓘ{J1}.
 /2 width=7 by lexs_inv_push2_aux/ qed-.
 
 (* Basic_2A1: includes lpx_sn_inv_pair *)
 lemma lexs_inv_next: ∀RN,RP,f,I1,I2,L1,L2.
-                     L1.â\93\98{I1} ⪤*[RN, RP, ⫯f] L2.ⓘ{I2} →
+                     L1.â\93\98{I1} ⪤*[RN, RP, â\86\91f] L2.ⓘ{I2} →
                      L1 ⪤*[RN, RP, f] L2 ∧ RN L1 I1 I2.
 #RN #RP #f #I1 #I2 #L1 #L2 #H elim (lexs_inv_next1 … H) -H
 #I0 #L0 #HL10 #HI10 #H destruct /2 width=1 by conj/
 qed-.
 
 lemma lexs_inv_push: ∀RN,RP,f,I1,I2,L1,L2.
-                     L1.â\93\98{I1} ⪤*[RN, RP, â\86\91f] L2.ⓘ{I2} →
+                     L1.â\93\98{I1} ⪤*[RN, RP, ⫯f] L2.ⓘ{I2} →
                      L1 ⪤*[RN, RP, f] L2 ∧ RP L1 I1 I2.
 #RN #RP #f #I1 #I2 #L1 #L2 #H elim (lexs_inv_push1 … H) -H
 #I0 #L0 #HL10 #HI10 #H destruct /2 width=1 by conj/