update in basic_2 and ground_2

[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 1ad709c9e3c39ab8a9d71cef719b8ba0ca248e33..f108bc5af9f5bc2fe04fe8bad7c102da228036ff 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/ideqsn_3.ma".
 include "basic_2/static/lfxs.ma".
 
 (* SYNTACTIC EQUIVALENCE FOR LOCAL ENVIRONMENTS ON REFERRED ENTRIES *********)
@@ -23,17 +23,15 @@ definition lfeq: relation3 term lenv lenv ≝
 
 interpretation
    "syntactic equivalence on referred entries (local environment)"
-   'LazyEqSn T L1 L2 = (lfeq T L1 L2).
+   'IdEqSn 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.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma lfeq_transitive_inv_lfxs: ∀R. lfeq_transitive R → lfxs_transitive ceq R R.
-/2 width=3 by/ qed-.
-
 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-.
@@ -78,11 +76,8 @@ qed-.
 
 (* Basic_properties *********************************************************)
 
-lemma lfxs_transitive_lfeq: ∀R. lfxs_transitive ceq R R → lfeq_transitive R.
-/2 width=5 by/ qed.
-
-lemma frees_lfeq_conf: ∀f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≡ f →
-                       ∀L2. L1 ≡[T] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
+lemma frees_lfeq_conf: ∀f,L1,T. L1 ⊢ 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