update in staic_2 and basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_lpx.ma
index cede8bf5296b71eab3f3a16bef43d9d2f27c3316..3d9b9081c711ae5e4fd04f94df5486239e93a830 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_lpx.ma
@@ -13,26 +13,33 @@
 (**************************************************************************)
 
 include "static_2/static/rex_lex.ma".
-include "basic_2/rt_transition/rpx_fsle.ma".
+include "basic_2/rt_transition/cpx_req.ma".
 include "basic_2/rt_transition/lpx.ma".
 
 (* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
 
 (* Properties with syntactic equivalence for referred local environments ****)
 
-lemma fleq_rpx (G):
-      ∀L1,L2,T. L1 ≡[T] L2 → ❪G,L1❫ ⊢ ⬈[T] L2.
+lemma req_rpx (G) (T):
+      ∀L1,L2. L1 ≡[T] L2 → ❪G,L1❫ ⊢ ⬈[T] L2.
 /2 width=1 by req_fwd_rex/ qed.
 
 (* Properties with extended rt-transition for full local envs ***************)
 
-lemma lpx_rpx (G):
-      ∀L1,L2,T. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L1❫ ⊢ ⬈[T] L2.
+lemma lpx_rpx (G) (T):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L1❫ ⊢ ⬈[T] L2.
 /2 width=1 by rex_lex/ qed.
 
 (* Inversion lemmas with extended rt-transition for full local envs *********)
 
-lemma rpx_inv_lpx_req (G):
-      ∀L1,L2,T. ❪G,L1❫ ⊢ ⬈[T] L2 →
+lemma rpx_inv_req_lpx (G) (T):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈[T] L2 →
+      ∃∃L. L1 ≡[T] L & ❪G,L❫ ⊢ ⬈ L2.
+/4 width=13 by cpx_req_conf, rex_inv_req_lex, rex_conf1_next/ qed-.
+
+(* Forward lemmas with extended rt-transition for full local envs ***********)
+
+lemma rpx_fwd_lpx_req (G) (T):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈[T] L2 →
       ∃∃L. ❪G,L1❫ ⊢ ⬈ L & L ≡[T] L2.
-/3 width=3 by rpx_fsge_comp, rex_inv_lex_req/ qed-.
+/3 width=3 by rpx_fsge_comp, rex_fwd_lex_req/ qed-.