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 7c8a4ae996807a73fbd171cce8ac2e8c347d5f58..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
@@ -13,23 +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".
 
-(* UNBOUND PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS ***********)
+(* EXTENDED PARALLEL RT-TRANSITION FOR REFERRED LOCAL ENVIRONMENTS **********)
 
 (* Properties with syntactic equivalence for referred local environments ****)
 
-lemma fleq_rpx (h) (G): ∀L1,L2,T. L1 ≡[T] L2 → ❪G,L1❫ ⊢ ⬈[h,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 unbound parallel rt-transition for full local envs *******)
+(* Properties with extended rt-transition for full local envs ***************)
 
-lemma lpx_rpx: ∀h,G,L1,L2,T. ❪G,L1❫ ⊢ ⬈[h] L2 → ❪G,L1❫ ⊢ ⬈[h,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 unbound parallel rt-transition for full local envs *)
+(* Inversion lemmas with extended rt-transition for full local envs *********)
 
-lemma rpx_inv_lpx_req: ∀h,G,L1,L2,T. ❪G,L1❫ ⊢ ⬈[h,T] L2 →
-                       ∃∃L. ❪G,L1❫ ⊢ ⬈[h] L & L ≡[T] L2.
-/3 width=3 by rpx_fsge_comp, rex_inv_lex_req/ qed-.
+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_fwd_lex_req/ qed-.