update in basic_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..684e57370908a1ac8abdd71a4b1b5b0c4d225043 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
@@ -25,15 +25,13 @@ interpretation
    "syntactic equivalence on referred entries (local environment)"
    'LazyEqSn 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-.
@@ -78,9 +76,6 @@ 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.
 #f #L1 #T #H elim H -f -L1 -T