X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Flfpx_lpx.ma;h=7ca9a2f28c74da9d240d15b03fe94aecc2b5abea;hb=5c186c72f508da0849058afeecc6877cd9ed6303;hp=a616027336b4306029108d72855f7b7effa4de02;hpb=268e7f336d036f77ffc9663358e9afda92b97730;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lpx.ma
index a61602733..7ca9a2f28 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lpx.ma
@@ -16,15 +16,20 @@ include "basic_2/static/lfxs_lex.ma".
 include "basic_2/rt_transition/lfpx_fsle.ma".
 include "basic_2/rt_transition/lpx.ma".
 
-(* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *****)
+(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
 
-(* Properties with uncounted parallel rt-transition for local environments **)
+(* Properties with syntactic equivalence for referred local environments ****)
 
-lemma lfpx_lpx: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
+lemma fleq_lfpx (h) (G): ∀L1,L2,T. L1 ≡[T] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
+/2 width=1 by lfeq_fwd_lfxs/ qed.
+
+(* Properties with unbound parallel rt-transition for full local envs *******)
+
+lemma lpx_lfpx: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T] L2.
 /2 width=1 by lfxs_lex/ qed.
 
-(* Inversion lemmas with uncounted parallel rt-transition for local envs ****)
+(* Inversion lemmas with unbound parallel rt-transition for full local envs *)
 
 lemma lfpx_inv_lpx_lfeq: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 →
-                         ∃∃L. ⦃G, L1⦄ ⊢ ⬈[h] L & L ≐[T] L2.
+                         ∃∃L. ⦃G, L1⦄ ⊢ ⬈[h] L & L ≡[T] L2.
 /3 width=3 by lfpx_fsge_comp, lfxs_inv_lex_lfeq/ qed-.