X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Ffpb.ma;h=245c10f530c4917564ed1e7be2dac1763370d2d9;hb=HEAD;hp=1ccc9ca6daa9162164d6a8d46e50405d640959ac;hpb=6167cca50de37eba76a062537b24f7caef5b34f2;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma
index 1ccc9ca6d..245c10f53 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma
@@ -12,31 +12,38 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/btpredproper_8.ma".
-include "basic_2/s_transition/fqu.ma".
-include "basic_2/static/lfdeq.ma".
-include "basic_2/rt_transition/lfpr_lfpx.ma".
+include "basic_2/notation/relations/predsubty_6.ma".
+include "static_2/s_transition/fquq.ma".
+include "basic_2/rt_transition/rpx.ma".
 
-(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+(* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
 
-inductive fpb (h) (o) (G1) (L1) (T1): relation3 genv lenv term ≝
-| fpb_fqu : ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ → fpb h o G1 L1 T1 G2 L2 T2
-| fpb_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → (T1 ≛[h, o] T2 → ⊥) → fpb h o G1 L1 T1 G1 L1 T2
-| fpb_lfpx: ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → (L1 ≛[h, o, T1] L2 → ⊥) → fpb h o G1 L1 T1 G1 L2 T1
-.
+(* Basic_2A1: uses: fpbq *)
+definition fpb (G1) (L1) (T1) (G2) (L2) (T2): Prop ≝
+           ∃∃L,T. ❨G1,L1,T1❩ ⬂⸮ ❨G2,L,T❩ & ❨G2,L❩ ⊢ T ⬈ T2 & ❨G2,L❩ ⊢ ⬈[T] L2.
 
 interpretation
-   "proper parallel rst-transition (closure)"
-   'BTPRedProper h o G1 L1 T1 G2 L2 T2 = (fpb h o G1 L1 T1 G2 L2 T2).
+  "parallel rst-transition (closure)"
+  'PRedSubTy G1 L1 T1 G2 L2 T2 = (fpb G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-(* Basic_2A1: includes: cpr_fpb *)
-lemma cpm_fpb: ∀n,h,o,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → (T1 ≛[h, o] T2 → ⊥) →
-               ⦃G, L, T1⦄ ≻[h, o] ⦃G, L, T2⦄.
-/3 width=2 by fpb_cpx, cpm_fwd_cpx/ qed.
+lemma fpb_intro (G1) (L1) (T1) (G2) (L2) (T2):
+      ∀L,T. ❨G1,L1,T1❩ ⬂⸮ ❨G2,L,T❩ → ❨G2,L❩ ⊢ T ⬈ T2 → 
+      ❨G2,L❩ ⊢ ⬈[T] L2 → ❨G1,L1,T1❩ ≽ ❨G2,L2,T2❩.
+/2 width=5 by ex3_2_intro/ qed.
 
-(* Basic_2A1: includes: lpr_fpb *)
-lemma lfpr_fpb: ∀h,o,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → (L1 ≛[h, o, T] L2 → ⊥) →
-                ⦃G, L1, T⦄ ≻[h, o] ⦃G, L2, T⦄.
-/3 width=1 by fpb_lfpx, lfpr_fwd_lfpx/ qed.
+lemma rpx_fpb (G) (T):
+      ∀L1,L2. ❨G,L1❩ ⊢ ⬈[T] L2 → ❨G,L1,T❩ ≽ ❨G,L2,T❩.
+/2 width=5 by fpb_intro/ qed.
+
+(* Basic inversion lemmas ***************************************************)
+
+lemma fpb_inv_gen (G1) (L1) (T1) (G2) (L2) (T2):
+      ❨G1,L1,T1❩ ≽ ❨G2,L2,T2❩ →
+      ∃∃L,T. ❨G1,L1,T1❩ ⬂⸮ ❨G2,L,T❩ & ❨G2,L❩ ⊢ T ⬈ T2 & ❨G2,L❩ ⊢ ⬈[T] L2.
+// qed-.
+
+(* Basic_2A1: removed theorems 2:
+              fpbq_fpbqa fpbqa_inv_fpbq
+*)