renaming

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
index aa2956699a2f5843037548398ebfe9ca17c1b149..747e9a511c5cf5eb11e454362772d21bd41dbe5b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
@@ -12,17 +12,18 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lazyeq_3.ma".
+include "basic_2/notation/relations/ideqsn_3.ma".
+include "basic_2/syntax/ceq_ext.ma".
 include "basic_2/relocation/lexs.ma".
 
 (* RANGED EQUIVALENCE FOR LOCAL ENVIRONMENTS ********************************)
 
 (* Basic_2A1: includes: lreq_atom lreq_zero lreq_pair lreq_succ *)
-definition lreq: relation3 rtmap lenv lenv ≝ lexs ceq cfull.
+definition lreq: relation3 rtmap lenv lenv ≝ lexs ceq_ext cfull.
 
 interpretation
   "ranged equivalence (local environment)"
-  'LazyEq f L1 L2 = (lreq f L1 L2).
+  'IdEqSn f L1 L2 = (lreq f L1 L2).
 
 (* Basic properties *********************************************************)
 
@@ -42,9 +43,7 @@ lemma lreq_refl: ∀f. reflexive … (lreq f).
 
 (* Basic_2A1: includes: lreq_sym *)
 lemma lreq_sym: ∀f. symmetric … (lreq f).
-#f #L1 #L2 #H elim H -L1 -L2 -f
-/2 width=1 by lexs_next, lexs_push/
-qed-.
+/3 width=2 by lexs_sym, cext2_sym/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
@@ -53,44 +52,50 @@ lemma lreq_inv_atom1: ∀f,Y. ⋆ ≡[f] Y → Y = ⋆.
 /2 width=4 by lexs_inv_atom1/ qed-.
 
 (* Basic_2A1: includes: lreq_inv_pair1 *)
-lemma lreq_inv_next1: ∀g,J,K1,Y,W1. K1.ⓑ{J}W1 ≡[⫯g] Y →
-                      ∃∃K2. K1 ≡[g] K2 & Y = K2.ⓑ{J}W1.
-#g #J #K1 #Y #W1 #H elim (lexs_inv_next1 … H) -H /2 width=3 by ex2_intro/
+lemma lreq_inv_next1: ∀g,J,K1,Y. K1.ⓘ{J} ≡[↑g] Y →
+                      ∃∃K2. K1 ≡[g] K2 & Y = K2.ⓘ{J}.
+#g #J #K1 #Y #H
+elim (lexs_inv_next1 … H) -H #Z #K2 #HK12 #H1 #H2 destruct
+<(ceq_ext_inv_eq … H1) -Z /2 width=3 by ex2_intro/
 qed-.
 
 (* Basic_2A1: includes: lreq_inv_zero1 lreq_inv_succ1 *)
-lemma lreq_inv_push1: ∀g,J,K1,Y,W1. K1.ⓑ{J}W1 ≡[↑g] Y →
-                      ∃∃K2,W2. K1 ≡[g] K2 & Y = K2.ⓑ{J}W2.
-#g #J #K1 #Y #W1 #H elim (lexs_inv_push1 … H) -H /2 width=4 by ex2_2_intro/ qed-.
+lemma lreq_inv_push1: ∀g,J1,K1,Y. K1.ⓘ{J1} ≡[⫯g] Y →
+                      ∃∃J2,K2. K1 ≡[g] K2 & Y = K2.ⓘ{J2}.
+#g #J1 #K1 #Y #H elim (lexs_inv_push1 … H) -H /2 width=4 by ex2_2_intro/
+qed-.
 
 (* Basic_2A1: includes: lreq_inv_atom2 *)
 lemma lreq_inv_atom2: ∀f,X. X ≡[f] ⋆ → X = ⋆.
 /2 width=4 by lexs_inv_atom2/ qed-.
 
 (* Basic_2A1: includes: lreq_inv_pair2 *)
-lemma lreq_inv_next2: ∀g,J,X,K2,W2. X ≡[⫯g] K2.ⓑ{J}W2 →
-                      ∃∃K1. K1 ≡[g] K2 & X = K1.ⓑ{J}W2.
-#g #J #X #K2 #W2 #H elim (lexs_inv_next2 … H) -H /2 width=3 by ex2_intro/ qed-.
+lemma lreq_inv_next2: ∀g,J,X,K2. X ≡[↑g] K2.ⓘ{J} →
+                      ∃∃K1. K1 ≡[g] K2 & X = K1.ⓘ{J}.
+#g #J #X #K2 #H
+elim (lexs_inv_next2 … H) -H #Z #K1 #HK12 #H1 #H2 destruct
+<(ceq_ext_inv_eq … H1) -J /2 width=3 by ex2_intro/
+qed-.
 
 (* Basic_2A1: includes: lreq_inv_zero2 lreq_inv_succ2 *)
-lemma lreq_inv_push2: ∀g,J,X,K2,W2. X ≡[↑g] K2.ⓑ{J}W2 →
-                      ∃∃K1,W1. K1 ≡[g] K2 & X = K1.ⓑ{J}W1.
-#g #J #X #K2 #W2 #H elim (lexs_inv_push2 … H) -H /2 width=4 by ex2_2_intro/ qed-.
+lemma lreq_inv_push2: ∀g,J2,X,K2. X ≡[⫯g] K2.ⓘ{J2} →
+                      ∃∃J1,K1. K1 ≡[g] K2 & X = K1.ⓘ{J1}.
+#g #J2 #X #K2 #H elim (lexs_inv_push2 … H) -H /2 width=4 by ex2_2_intro/
+qed-.
 
 (* Basic_2A1: includes: lreq_inv_pair *)
-lemma lreq_inv_next: ∀f,I1,I2,L1,L2,V1,V2.
-                     L1.ⓑ{I1}V1 ≡[⫯f] (L2.ⓑ{I2}V2) →
-                     ∧∧ L1 ≡[f] L2 & V1 = V2 & I1 = I2.
-/2 width=1 by lexs_inv_next/ qed-.
+lemma lreq_inv_next: ∀f,I1,I2,L1,L2. L1.ⓘ{I1} ≡[↑f] L2.ⓘ{I2} →
+                     L1 ≡[f] L2 ∧ I1 = I2.
+#f #I1 #I2 #L1 #L2 #H elim (lexs_inv_next … H) -H
+/3 width=3 by ceq_ext_inv_eq, conj/
+qed-.
 
 (* Basic_2A1: includes: lreq_inv_succ *)
-lemma lreq_inv_push: ∀f,I1,I2,L1,L2,V1,V2.
-                     L1.ⓑ{I1}V1 ≡[↑f] (L2.ⓑ{I2}V2) →
-                     L1 ≡[f] L2 ∧ I1 = I2.
-#f #I1 #I2 #L1 #L2 #V1 #V2 #H elim (lexs_inv_push … H) -H /2 width=1 by conj/
+lemma lreq_inv_push: ∀f,I1,I2,L1,L2. L1.ⓘ{I1} ≡[⫯f] L2.ⓘ{I2} → L1 ≡[f] L2.
+#f #I1 #I2 #L1 #L2 #H elim (lexs_inv_push … H) -H /2 width=1 by conj/
 qed-.
 
-lemma lreq_inv_tl: ∀f,I,L1,L2,V. L1 ≡[⫱f] L2 → L1.ⓑ{I}V ≡[f] L2.ⓑ{I}V.
+lemma lreq_inv_tl: ∀f,I,L1,L2. L1 ≡[⫱f] L2 → L1.ⓘ{I} ≡[f] L2.ⓘ{I}.
 /2 width=1 by lexs_inv_tl/ qed-.
 
 (* Basic_2A1: removed theorems 5: