milestone update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbc.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbc.ma
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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/notation/relations/predsubtyproper_6.ma".
+include "static_2/static/feqx.ma".
+include "basic_2/rt_transition/fpb.ma".
+
+(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+
+(* Basic_2A1: uses: fpb *)
+definition fpbc (G1) (L1) (T1) (G2) (L2) (T2): Prop ≝
+           ∧∧ ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫
+            & (❪G1,L1,T1❫ ≅ ❪G2,L2,T2❫ → ⊥).
+
+interpretation
+  "proper parallel rst-transition (closure)"
+  'PRedSubTyProper G1 L1 T1 G2 L2 T2 = (fpbc G1 L1 T1 G2 L2 T2).
+
+(* Basic properties *********************************************************)
+
+(* Basic_2A1: fpbq_inv_fpb_alt *)
+lemma fpbc_intro (G1) (L1) (T1) (G2) (L2) (T2):
+      ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ → (❪G1,L1,T1❫ ≅ ❪G2,L2,T2❫ → ⊥) →
+      ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
+/3 width=1 by conj/ qed.
+
+lemma rpx_fpbc (G) (T):
+      ∀L1,L2. ❪G,L1❫ ⊢ ⬈[T] L2 → (L1 ≅[T] L2 → ⊥) → ❪G,L1,T❫ ≻ ❪G,L2,T❫.
+/4 width=4 by fpbc_intro, rpx_fpb, feqg_fwd_reqg_sn/ qed.  
+
+(* Basic inversion lemmas ***************************************************)
+
+(* Basic_2A1: uses: fpb_fpbq_alt *)
+lemma fpbc_inv_gen (S):
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
+      ∧∧ ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ & (❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ⊥).
+#S #G1 #G2 #L1 #L2 #T1 #T2 *
+/4 width=2 by feqg_feqx, conj/
+qed-.
+
+(* Basic forward lemmas *****************************************************)
+
+(* Basic_2A1: uses: fpb_fpbq *)
+lemma fpbc_fwd_fpb:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
+      ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫.
+#G1 #G2 #L1 #L2 #T1 #T2 * //
+qed-.