update in staic_2 and basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_reqx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_reqx.ma
index 73f134d10014a59627116e09309c095791cb00e2..dfd3672410eec66fc9fbf97bf3f5c497862ca145 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_reqx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx_reqx.ma
@@ -20,14 +20,37 @@ include "basic_2/rt_transition/rpx_lpx.ma".
 
 (* Properties with sort-irrelevant equivalence for local environments *******)
 
-(**) (* to update as reqx_rpx_trans *)
+lemma reqx_lpx_trans_rpx (G) (L) (T:term):
+      ∀L1. L1 ≛[T] L → ∀L2. ❪G,L❫ ⊢ ⬈ L2 → ❪G,L❫ ⊢ ⬈[T] L2.
+/3 width=1 by lpx_rpx, reqx_rpx_trans/ qed.
+
 (* Basic_2A1: uses: lleq_lpx_trans *)
 lemma reqx_lpx_trans (G):
       ∀L2,K2. ❪G,L2❫ ⊢ ⬈ K2 → ∀L1. ∀T:term. L1 ≛[T] L2 →
       ∃∃K1. ❪G,L1❫ ⊢ ⬈ K1 & K1 ≛[T] K2.
 #G #L2 #K2 #HLK2 #L1 #T #HL12
-lapply (lpx_rpx … T HLK2) -HLK2 #HLK2
+lapply (lpx_rpx … T … HLK2) -HLK2 #HLK2
 lapply (reqx_rpx_trans … HL12 … HLK2) -L2 #H
-elim (rpx_inv_lpx_req … H) -H #K1 #HLK1 #HK12
+elim (rpx_fwd_lpx_req … H) -H #K1 #HLK1 #HK12
+/3 width=3 by req_reqx, ex2_intro/
+qed-.
+
+(* Inversion lemmas with sort-irrelevant equivalence for local environments *)
+
+lemma rpx_inv_reqx_lpx (G) (T):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈[T] L2 →
+      ∃∃L. L1 ≛[T] L & ❪G,L❫ ⊢ ⬈ L2.
+#G #T #L1 #L2 #H
+elim (rpx_inv_req_lpx … H) -H #L #HL1 #HL2
+/3 width=3 by req_reqx, ex2_intro/
+qed-.
+
+(* Forward lemmas with sort-irrelevant equivalence for local environments ***)
+
+lemma rpx_fwd_lpx_reqx (G) (T):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈[T] L2 →
+      ∃∃L. ❪G,L1❫ ⊢ ⬈ L & L ≛[T] L2.
+#G #T #L1 #L2 #H
+elim (rpx_fwd_lpx_req … H) -H #L #HL1 #HL2
 /3 width=3 by req_reqx, ex2_intro/
 qed-.