X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Flfeq.ma;h=c248d2acb2516510535d804e041ab95ede00091d;hp=684e57370908a1ac8abdd71a4b1b5b0c4d225043;hb=268e7f336d036f77ffc9663358e9afda92b97730;hpb=1604f2ee65c57eefb7c6b3122eab2a9f32e0552d

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
index 684e57370..c248d2acb 100644
--- 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. ∀L2,T1,T2. R L2 T1 T2 → ∀L1. L1 ≡[T1] L2 → R L1 T1 T2.
+           λR. ∀L2,T1,T2. R L2 T1 T2 → ∀L1. L1 ≐[T1] L2 → R L1 T1 T2.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lfeq_inv_bind: ∀p,I,L1,L2,V,T. L1 ≡[ⓑ{p,I}V.T] L2 →
-                     ∧∧ L1 ≡[V] L2 & L1.ⓑ{I}V ≡[T] L2.ⓑ{I}V.
+lemma lfeq_inv_bind: ∀p,I,L1,L2,V,T. L1 ≐[ⓑ{p,I}V.T] L2 →
+                     ∧∧ L1 ≐[V] L2 & L1.ⓑ{I}V ≐[T] L2.ⓑ{I}V.
 /2 width=2 by lfxs_inv_bind/ qed-.
 
-lemma lfeq_inv_flat: ∀I,L1,L2,V,T. L1 ≡[ⓕ{I}V.T] L2 →
-                     ∧∧ L1 ≡[V] L2 & L1 ≡[T] L2.
+lemma lfeq_inv_flat: ∀I,L1,L2,V,T. L1 ≐[ⓕ{I}V.T] L2 →
+                     ∧∧ L1 ≐[V] L2 & L1 ≐[T] L2.
 /2 width=2 by lfxs_inv_flat/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma lfeq_inv_zero_pair_sn: ∀I,L2,K1,V. K1.ⓑ{I}V ≡[#0] L2 →
-                             ∃∃K2. K1 ≡[V] K2 & L2 = K2.ⓑ{I}V.
+lemma lfeq_inv_zero_pair_sn: ∀I,L2,K1,V. K1.ⓑ{I}V ≐[#0] L2 →
+                             ∃∃K2. K1 ≐[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: ∀I,L1,K2,V. L1 ≡[#0] K2.ⓑ{I}V →
-                             ∃∃K1. K1 ≡[V] K2 & L1 = K1.ⓑ{I}V.
+lemma lfeq_inv_zero_pair_dx: ∀I,L1,K2,V. L1 ≐[#0] K2.ⓑ{I}V →
+                             ∃∃K1. K1 ≐[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: ∀I1,K1,L2,i. K1.ⓘ{I1} ≡[#⫯i] L2 →
-                             ∃∃I2,K2. K1 ≡[#i] K2 & L2 = K2.ⓘ{I2}.
+lemma lfeq_inv_lref_bind_sn: ∀I1,K1,L2,i. K1.ⓘ{I1} ≐[#⫯i] L2 →
+                             ∃∃I2,K2. K1 ≐[#i] K2 & L2 = K2.ⓘ{I2}.
 /2 width=2 by lfxs_inv_lref_bind_sn/ qed-.
 
-lemma lfeq_inv_lref_bind_dx: ∀I2,K2,L1,i. L1 ≡[#⫯i] K2.ⓘ{I2} →
-                             ∃∃I1,K1. K1 ≡[#i] K2 & L1 = K1.ⓘ{I1}.
+lemma lfeq_inv_lref_bind_dx: ∀I2,K2,L1,i. L1 ≐[#⫯i] K2.ⓘ{I2} →
+                             ∃∃I1,K1. K1 ≐[#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 →
-                     ∀L1,L2,T. L1 ≡[T] L2 → L1 ⪤*[R, T] L2.
+                     ∀L1,L2,T. L1 ≐[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 →
-                       ∀L2. L1 ≡[T] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
+                       ∀L2. L1 ≐[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