X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Ffpb.ma;h=9d9af6c964e232c6c43eb1e11ffea4c3053e7dbb;hb=e23331eef5817eaa6c5e1c442d1d6bbb18650573;hp=f0e7362b225704f5db6dc24b3b4da5edb9900ba9;hpb=a9e994f4ca8e04743c53ed8cb057ee5dae80c8f9;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 f0e7362b2..9d9af6c96 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb.ma
@@ -12,30 +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_lpx: ∀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.
 
-lemma lpr_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_lpx, 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
+*)