update in basic_2 + web page

[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 cc3e75b0a5107964bdd5b503c9e8904aca6fa0d4..1ec062b82f3d048edea7b52cddde230137ae75fb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lreq.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lazyeqsn_3.ma".
+include "basic_2/notation/relations/doteqsn_3.ma".
 include "basic_2/syntax/ceq_ext.ma".
 include "basic_2/relocation/lexs.ma".
 
@@ -23,18 +23,18 @@ definition lreq: relation3 rtmap lenv lenv ≝ lexs ceq_ext cfull.
 
 interpretation
   "ranged equivalence (local environment)"
-  'LazyEqSn f L1 L2 = (lreq f L1 L2).
+  'DotEqSn f L1 L2 = (lreq f L1 L2).
 
 (* Basic properties *********************************************************)
 
-lemma lreq_eq_repl_back: â\88\80L1,L2. eq_repl_back â\80¦ (λf. L1 â\89¡[f] L2).
+lemma lreq_eq_repl_back: â\88\80L1,L2. eq_repl_back â\80¦ (λf. L1 â\89\90[f] L2).
 /2 width=3 by lexs_eq_repl_back/ qed-.
 
-lemma lreq_eq_repl_fwd: â\88\80L1,L2. eq_repl_fwd â\80¦ (λf. L1 â\89¡[f] L2).
+lemma lreq_eq_repl_fwd: â\88\80L1,L2. eq_repl_fwd â\80¦ (λf. L1 â\89\90[f] L2).
 /2 width=3 by lexs_eq_repl_fwd/ qed-.
 
-lemma sle_lreq_trans: â\88\80f2,L1,L2. L1 â\89¡[f2] L2 →
-                      â\88\80f1. f1 â\8a\86 f2 â\86\92 L1 â\89¡[f1] L2.
+lemma sle_lreq_trans: â\88\80f2,L1,L2. L1 â\89\90[f2] L2 →
+                      â\88\80f1. f1 â\8a\86 f2 â\86\92 L1 â\89\90[f1] L2.
 /2 width=3 by sle_lexs_trans/ qed-.
 
 (* Basic_2A1: includes: lreq_refl *)
@@ -48,54 +48,54 @@ lemma lreq_sym: ∀f. symmetric … (lreq f).
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: includes: lreq_inv_atom1 *)
-lemma lreq_inv_atom1: â\88\80f,Y. â\8b\86 â\89¡[f] Y → Y = ⋆.
+lemma lreq_inv_atom1: â\88\80f,Y. â\8b\86 â\89\90[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 →
-                      â\88\83â\88\83K2. K1 â\89¡[g] K2 & Y = K2.ⓘ{J}.
+lemma lreq_inv_next1: â\88\80g,J,K1,Y. K1.â\93\98{J} â\89\90[⫯g] Y →
+                      â\88\83â\88\83K2. K1 â\89\90[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: â\88\80g,J1,K1,Y. K1.â\93\98{J1} â\89¡[↑g] Y →
-                      â\88\83â\88\83J2,K2. K1 â\89¡[g] K2 & Y = K2.ⓘ{J2}.
+lemma lreq_inv_push1: â\88\80g,J1,K1,Y. K1.â\93\98{J1} â\89\90[↑g] Y →
+                      â\88\83â\88\83J2,K2. K1 â\89\90[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: â\88\80f,X. X â\89¡[f] ⋆ → X = ⋆.
+lemma lreq_inv_atom2: â\88\80f,X. X â\89\90[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} →
-                      â\88\83â\88\83K1. K1 â\89¡[g] K2 & X = K1.ⓘ{J}.
+lemma lreq_inv_next2: â\88\80g,J,X,K2. X â\89\90[⫯g] K2.ⓘ{J} →
+                      â\88\83â\88\83K1. K1 â\89\90[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: â\88\80g,J2,X,K2. X â\89¡[↑g] K2.ⓘ{J2} →
-                      â\88\83â\88\83J1,K1. K1 â\89¡[g] K2 & X = K1.ⓘ{J1}.
+lemma lreq_inv_push2: â\88\80g,J2,X,K2. X â\89\90[↑g] K2.ⓘ{J2} →
+                      â\88\83â\88\83J1,K1. K1 â\89\90[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} →
-                     L1 â\89¡[f] L2 ∧ I1 = I2.
+lemma lreq_inv_next: â\88\80f,I1,I2,L1,L2. L1.â\93\98{I1} â\89\90[⫯f] L2.ⓘ{I2} →
+                     L1 â\89\90[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: â\88\80f,I1,I2,L1,L2. L1.â\93\98{I1} â\89¡[â\86\91f] L2.â\93\98{I2} â\86\92 L1 â\89¡[f] L2.
+lemma lreq_inv_push: â\88\80f,I1,I2,L1,L2. L1.â\93\98{I1} â\89\90[â\86\91f] L2.â\93\98{I2} â\86\92 L1 â\89\90[f] L2.
 #f #I1 #I2 #L1 #L2 #H elim (lexs_inv_push … H) -H /2 width=1 by conj/
 qed-.
 
-lemma lreq_inv_tl: â\88\80f,I,L1,L2. L1 â\89¡[⫱f] L2 â\86\92 L1.â\93\98{I} â\89¡[f] L2.ⓘ{I}.
+lemma lreq_inv_tl: â\88\80f,I,L1,L2. L1 â\89\90[⫱f] L2 â\86\92 L1.â\93\98{I} â\89\90[f] L2.ⓘ{I}.
 /2 width=1 by lexs_inv_tl/ qed-.
 
 (* Basic_2A1: removed theorems 5: