renaming

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lfpx_lpx.ma

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 7fa9f9508b5d0e6b4a9cc26de297825f0d639486..7ca9a2f28c74da9d240d15b03fe94aecc2b5abea 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lpx.ma
@@ -16,14 +16,19 @@ include "basic_2/static/lfxs_lex.ma".
 include "basic_2/rt_transition/lfpx_fsle.ma".
 include "basic_2/rt_transition/lpx.ma".
 
-(* UNBOUND PARALLEL RT-TRANSITION FOR LOCAL ENV.S ON REFERRED ENTRIES *******)
+(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
 
-(* Properties with unbound 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 unbound 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.