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 e0b7d236c0b5e7f05e1430211800cd9891cb768a..747e9a511c5cf5eb11e454362772d21bd41dbe5b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
@@ -12,18 +12,18 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lazyeqsn_3.ma".
-include "basic_2/syntax/ext2.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)"
-  'LazyEqSn f L1 L2 = (lreq f L1 L2).
+  'IdEqSn f L1 L2 = (lreq f L1 L2).
 
 (* Basic properties *********************************************************)
 
@@ -39,11 +39,11 @@ lemma sle_lreq_trans: ∀f2,L1,L2. L1 ≡[f2] L2 →
 
 (* 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 ***************************************************)
 
@@ -52,13 +52,15 @@ 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: â\88\80g,J,K1,Y. K1.â\93\98{J} â\89¡[⫯g] Y →
+lemma lreq_inv_next1: â\88\80g,J,K1,Y. K1.â\93\98{J} â\89¡[â\86\91g] 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/
+#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: â\88\80g,J1,K1,Y. K1.â\93\98{J1} â\89¡[â\86\91g] Y →
+lemma lreq_inv_push1: â\88\80g,J1,K1,Y. K1.â\93\98{J1} â\89¡[⫯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-.
@@ -68,24 +70,28 @@ 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: â\88\80g,J,X,K2. X â\89¡[⫯g] K2.ⓘ{J} →
+lemma lreq_inv_next2: â\88\80g,J,X,K2. X â\89¡[â\86\91g] 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/
+#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: â\88\80g,J2,X,K2. X â\89¡[â\86\91g] K2.ⓘ{J2} →
+lemma lreq_inv_push2: â\88\80g,J2,X,K2. X â\89¡[⫯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: â\88\80f,I1,I2,L1,L2. L1.â\93\98{I1} â\89¡[⫯f] L2.ⓘ{I2} →
+lemma lreq_inv_next: â\88\80f,I1,I2,L1,L2. L1.â\93\98{I1} â\89¡[â\86\91f] L2.ⓘ{I2} →
                      L1 ≡[f] L2 ∧ I1 = I2.
-/2 width=1 by lexs_inv_next/ qed-.
+#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: â\88\80f,I1,I2,L1,L2. L1.â\93\98{I1} â\89¡[â\86\91f] L2.ⓘ{I2} → L1 ≡[f] L2.
+lemma lreq_inv_push: â\88\80f,I1,I2,L1,L2. L1.â\93\98{I1} â\89¡[⫯f] L2.ⓘ{I2} → L1 ≡[f] L2.
 #f #I1 #I2 #L1 #L2 #H elim (lexs_inv_push … H) -H /2 width=1 by conj/
 qed-.