update in basic_2 + web page

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / static / lfeq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
index 684e57370908a1ac8abdd71a4b1b5b0c4d225043..c248d2acb2516510535d804e041ab95ede00091d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/lazyeqsn_3.ma".
+include "basic_2/notation/relations/doteqsn_3.ma".
 include "basic_2/static/lfxs.ma".
 
 (* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
@@ -23,45 +23,45 @@ definition lfeq: relation3 term lenv lenv ≝
 
 interpretation
    "syntactic equivalence on referred entries (local environment)"
-   'LazyEqSn T L1 L2 = (lfeq T L1 L2).
+   'DotEqSn T L1 L2 = (lfeq T L1 L2).
 
 (* Note: "lfeq_transitive R" is equivalent to "lfxs_transitive ceq R R" *)
 (* Basic_2A1: uses: lleq_transitive *)
 definition lfeq_transitive: predicate (relation3 lenv term term) ≝
-           λR. â\88\80L2,T1,T2. R L2 T1 T2 â\86\92 â\88\80L1. L1 â\89¡[T1] L2 → R L1 T1 T2.
+           λR. â\88\80L2,T1,T2. R L2 T1 T2 â\86\92 â\88\80L1. L1 â\89\90[T1] L2 → R L1 T1 T2.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lfeq_inv_bind: â\88\80p,I,L1,L2,V,T. L1 â\89¡[ⓑ{p,I}V.T] L2 →
-                     â\88§â\88§ L1 â\89¡[V] L2 & L1.â\93\91{I}V â\89¡[T] L2.ⓑ{I}V.
+lemma lfeq_inv_bind: â\88\80p,I,L1,L2,V,T. L1 â\89\90[ⓑ{p,I}V.T] L2 →
+                     â\88§â\88§ L1 â\89\90[V] L2 & L1.â\93\91{I}V â\89\90[T] L2.ⓑ{I}V.
 /2 width=2 by lfxs_inv_bind/ qed-.
 
-lemma lfeq_inv_flat: â\88\80I,L1,L2,V,T. L1 â\89¡[ⓕ{I}V.T] L2 →
-                     â\88§â\88§ L1 â\89¡[V] L2 & L1 â\89¡[T] L2.
+lemma lfeq_inv_flat: â\88\80I,L1,L2,V,T. L1 â\89\90[ⓕ{I}V.T] L2 →
+                     â\88§â\88§ L1 â\89\90[V] L2 & L1 â\89\90[T] L2.
 /2 width=2 by lfxs_inv_flat/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma lfeq_inv_zero_pair_sn: â\88\80I,L2,K1,V. K1.â\93\91{I}V â\89¡[#0] L2 →
-                             â\88\83â\88\83K2. K1 â\89¡[V] K2 & L2 = K2.ⓑ{I}V.
+lemma lfeq_inv_zero_pair_sn: â\88\80I,L2,K1,V. K1.â\93\91{I}V â\89\90[#0] L2 →
+                             â\88\83â\88\83K2. K1 â\89\90[V] K2 & L2 = K2.ⓑ{I}V.
 #I #L2 #K1 #V #H
 elim (lfxs_inv_zero_pair_sn … H) -H #K2 #X #HK12 #HX #H destruct
 /2 width=3 by ex2_intro/
 qed-.
 
-lemma lfeq_inv_zero_pair_dx: â\88\80I,L1,K2,V. L1 â\89¡[#0] K2.ⓑ{I}V →
-                             â\88\83â\88\83K1. K1 â\89¡[V] K2 & L1 = K1.ⓑ{I}V.
+lemma lfeq_inv_zero_pair_dx: â\88\80I,L1,K2,V. L1 â\89\90[#0] K2.ⓑ{I}V →
+                             â\88\83â\88\83K1. K1 â\89\90[V] K2 & L1 = K1.ⓑ{I}V.
 #I #L1 #K2 #V #H
 elim (lfxs_inv_zero_pair_dx … H) -H #K1 #X #HK12 #HX #H destruct
 /2 width=3 by ex2_intro/
 qed-.
 
-lemma lfeq_inv_lref_bind_sn: â\88\80I1,K1,L2,i. K1.â\93\98{I1} â\89¡[#⫯i] L2 →
-                             â\88\83â\88\83I2,K2. K1 â\89¡[#i] K2 & L2 = K2.ⓘ{I2}.
+lemma lfeq_inv_lref_bind_sn: â\88\80I1,K1,L2,i. K1.â\93\98{I1} â\89\90[#⫯i] L2 →
+                             â\88\83â\88\83I2,K2. K1 â\89\90[#i] K2 & L2 = K2.ⓘ{I2}.
 /2 width=2 by lfxs_inv_lref_bind_sn/ qed-.
 
-lemma lfeq_inv_lref_bind_dx: â\88\80I2,K2,L1,i. L1 â\89¡[#⫯i] K2.ⓘ{I2} →
-                             â\88\83â\88\83I1,K1. K1 â\89¡[#i] K2 & L1 = K1.ⓘ{I1}.
+lemma lfeq_inv_lref_bind_dx: â\88\80I2,K2,L1,i. L1 â\89\90[#⫯i] K2.ⓘ{I2} →
+                             â\88\83â\88\83I1,K1. K1 â\89\90[#i] K2 & L1 = K1.ⓘ{I1}.
 /2 width=2 by lfxs_inv_lref_bind_dx/ qed-.
 
 (* Basic forward lemmas *****************************************************)
@@ -69,7 +69,7 @@ lemma lfeq_inv_lref_bind_dx: ∀I2,K2,L1,i. L1 ≡[#⫯i] K2.ⓘ{I2} →
 (* Basic_2A1: was: llpx_sn_lrefl *)
 (* Note: this should have been lleq_fwd_llpx_sn *)
 lemma lfeq_fwd_lfxs: ∀R. c_reflexive … R →
-                     â\88\80L1,L2,T. L1 â\89¡[T] L2 → L1 ⪤*[R, T] L2.
+                     â\88\80L1,L2,T. L1 â\89\90[T] L2 → L1 ⪤*[R, T] L2.
 #R #HR #L1 #L2 #T * #f #Hf #HL12
 /4 width=7 by lexs_co, cext2_co, ex2_intro/
 qed-.
@@ -77,7 +77,7 @@ qed-.
 (* Basic_properties *********************************************************)
 
 lemma frees_lfeq_conf: ∀f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≡ f →
-                       â\88\80L2. L1 â\89¡[T] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
+                       â\88\80L2. L1 â\89\90[T] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
 #f #L1 #T #H elim H -f -L1 -T
 [ /2 width=3 by frees_sort/
 | #f #i #Hf #L2 #H2