X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flreq.ma;h=1ec062b82f3d048edea7b52cddde230137ae75fb;hb=268e7f336d036f77ffc9663358e9afda92b97730;hp=6f8e3bc74cc3ca54b622c01d8b6f1a3b3323666e;hpb=98fbba1b68d457807c73ebf70eb2a48696381da4;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
index 6f8e3bc74..1ec062b82 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
@@ -12,84 +12,90 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lazyeq_3.ma".
-include "basic_2/syntax/ext2.ma".
+include "basic_2/notation/relations/doteqsn_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).
+  'DotEqSn f L1 L2 = (lreq f L1 L2).
 
 (* Basic properties *********************************************************)
 
-lemma lreq_eq_repl_back: ∀L1,L2. eq_repl_back … (λf. L1 ≡[f] L2).
+lemma lreq_eq_repl_back: ∀L1,L2. eq_repl_back … (λf. L1 ≐[f] L2).
 /2 width=3 by lexs_eq_repl_back/ qed-.
 
-lemma lreq_eq_repl_fwd: ∀L1,L2. eq_repl_fwd … (λf. L1 ≡[f] L2).
+lemma lreq_eq_repl_fwd: ∀L1,L2. eq_repl_fwd … (λf. L1 ≐[f] L2).
 /2 width=3 by lexs_eq_repl_fwd/ qed-.
 
-lemma sle_lreq_trans: ∀f2,L1,L2. L1 ≡[f2] L2 →
-                      ∀f1. f1 ⊆ f2 → L1 ≡[f1] L2.
+lemma sle_lreq_trans: ∀f2,L1,L2. L1 ≐[f2] L2 →
+                      ∀f1. f1 ⊆ f2 → L1 ≐[f1] L2.
 /2 width=3 by sle_lexs_trans/ qed-.
 
 (* Basic_2A1: includes: lreq_refl *)
 lemma lreq_refl: ∀f. reflexive … (lreq f).
-/3 width=1 by lexs_refl, ext2_refl/ qed.
+/2 width=1 by lexs_refl/ qed.
 
 (* Basic_2A1: includes: lreq_sym *)
 lemma lreq_sym: ∀f. symmetric … (lreq f).
-/3 width=1 by lexs_sym, ext2_sym/ qed-.
+/3 width=2 by lexs_sym, cext2_sym/ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: includes: lreq_inv_atom1 *)
-lemma lreq_inv_atom1: ∀f,Y. ⋆ ≡[f] Y → Y = ⋆.
+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. K1.ⓘ{J} ≡[⫯g] Y →
-                      ∃∃K2. K1 ≡[g] K2 & Y = K2.ⓘ{J}.
-#g #J #K1 #Y #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,J1,K1,Y. K1.ⓘ{J1} ≡[↑g] Y →
-                      ∃∃J2,K2. K1 ≡[g] K2 & Y = K2.ⓘ{J2}.
+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 = ⋆.
+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. X ≡[⫯g] K2.ⓘ{J} →
-                      ∃∃K1. K1 ≡[g] K2 & X = K1.ⓘ{J}.
-#g #J #X #K2 #H elim (lexs_inv_next2 … H) -H /2 width=3 by ex2_intro/
+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,J2,X,K2. X ≡[↑g] K2.ⓘ{J2} →
-                      ∃∃J1,K1. K1 ≡[g] K2 & X = K1.ⓘ{J1}.
+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. L1.ⓘ{I1} ≡[⫯f] L2.ⓘ{I2} →
-                     L1 ≡[f] L2 ∧ 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. L1.ⓘ{I1} ≡[↑f] L2.ⓘ{I2} → L1 ≡[f] L2.
+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. L1 ≡[⫱f] L2 → L1.ⓘ{I} ≡[f] L2.ⓘ{I}.
+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: