- equivalene of tc_lfxs and lex + lfeq proved

[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 cc3fce365629f263bcccd1faa243aa485a0628a0..1b625752029bb6cdb6b5864a500d72c308e82ea2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfeq.ma
@@ -25,10 +25,29 @@ interpretation
    "syntactic equivalence on referred entries (local environment)"
    'LazyEqSn T L1 L2 = (lfeq T L1 L2).
 
-(***************************************************)
+(* 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.
 
-axiom lfeq_lfxs_trans: ∀R,L1,L,T. L1 ≡[T] L →
-                       ∀L2. L ⪤*[R, T] L2 → L1 ⪤*[R, T] L2.
+(* Basic_properties *********************************************************)
+
+lemma lfxs_transitive_lfeq: ∀R. lfxs_transitive ceq R R → lfeq_transitive R.
+/2 width=5 by/ qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma lfeq_transitive_inv_lfxs: ∀R. lfeq_transitive R → lfxs_transitive ceq R R.
+/2 width=3 by/ qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+(* 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.
+#R #HR #L1 #L2 #T * #f #Hf #HL12
+/4 width=7 by lexs_co, cext2_co, ex2_intro/
+qed-.
 
 (* Basic_2A1: removed theorems 10:
               lleq_ind lleq_fwd_lref