milestone update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lpx.ma
new file mode 100644 (file)
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/rt_transition/rpx_lpx.ma".
+include "basic_2/rt_transition/fpb.ma".
+
+(* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
+
+(* Properties with extended rt-transition for full local envs ***************)
+
+(* Basic_2A1: uses: fpbq_lpx *)
+lemma lpx_fpb (G) (T):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈ L2 → ❪G,L1,T❫ ≽ ❪G,L2,T❫.
+/3 width=1 by rpx_fpb, lpx_rpx/ qed.
+
+lemma fpb_intro_req (G1) (G2) (L1) (L2) (T1) (T2):
+      ∀L0,L,T. ❪G1,L1,T1❫ ⬂⸮ ❪G2,L,T❫ → ❪G2,L❫ ⊢ T ⬈ T2 → 
+      L ≡[T] L0 → ❪G2,L0❫ ⊢ ⬈ L2 → ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫.
+/4 width=10 by fpb_intro, lpx_rpx, reqg_rpx_trans/ qed.
+
+(* Inversion lemmas with extended rt-transition for full local envs *********)
+
+lemma fpb_inv_req (G1) (G2) (L1) (L2) (T1) (T2):
+      ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
+      ∃∃L0,L,T. ❪G1,L1,T1❫ ⬂⸮ ❪G2,L,T❫ & ❪G2,L❫ ⊢ T ⬈ T2 & L ≡[T] L0 & ❪G2,L0❫ ⊢ ⬈ L2.
+#G1 #G2 #L1 #L2 #T1 #T2 * #L #T #H1 #HT2 #HL2
+elim (rpx_inv_req_lpx … HL2) -HL2 #L0 #HL0 #HL02
+/2 width=7 by ex4_3_intro/
+qed-.
+
+(* Forward lemmas with extended rt-transition for full local envs ***********)
+
+lemma fpb_fwd_req (G1) (G2) (L1) (L2) (T1) (T2):
+      ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
+      ∃∃L0,L,T. ❪G1,L1,T1❫ ⬂⸮ ❪G2,L,T❫ & ❪G2,L❫ ⊢ T ⬈ T2 & ❪G2,L❫ ⊢ ⬈ L0 & L0 ≡[T] L2.
+#G1 #G2 #L1 #L2 #T1 #T2 * #L #T #H1 #HT2 #HL2
+elim (rpx_fwd_lpx_req … HL2) -HL2 #L0 #HL0 #HL02
+/2 width=7 by ex4_3_intro/
+qed-.