X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Ffpbs.ma;h=64277054e8743037228017ba317762f90ea05864;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=2b13efb0e361d321039ece7f0179b4f6ac2fa61f;hpb=54c9014b6657403c6e235c652176218e750d4b8a;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
index 2b13efb0e..64277054e 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
@@ -13,59 +13,63 @@
 (**************************************************************************)
 
 include "ground_2/lib/star.ma".
-include "basic_2/notation/relations/predsubtystar_8.ma".
+include "basic_2/notation/relations/predsubtystar_7.ma".
 include "basic_2/rt_transition/fpbq.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
 
-definition fpbs: ∀h. sd h → tri_relation genv lenv term ≝
-                 λh,o. tri_TC … (fpbq h o).
+definition fpbs: ∀h. tri_relation genv lenv term ≝
+                 λh. tri_TC … (fpbq h).
 
 interpretation "parallel rst-computation (closure)"
-   'PRedSubTyStar  h o G1 L1 T1 G2 L2 T2 = (fpbs h o G1 L1 T1 G2 L2 T2).
+   'PRedSubTyStar  h G1 L1 T1 G2 L2 T2 = (fpbs h G1 L1 T1 G2 L2 T2).
 
 (* Basic eliminators ********************************************************)
 
-lemma fpbs_ind: ∀h,o,G1,L1,T1. ∀R:relation3 genv lenv term. R G1 L1 T1 →
-                (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, o] ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
-                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → R G2 L2 T2.
+lemma fpbs_ind: ∀h,G1,L1,T1. ∀Q:relation3 genv lenv term. Q G1 L1 T1 →
+                (∀G,G2,L,L2,T,T2. ❪G1,L1,T1❫ ≥[h] ❪G,L,T❫ → ❪G,L,T❫ ≽[h] ❪G2,L2,T2❫ → Q G L T → Q G2 L2 T2) →
+                ∀G2,L2,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ → Q G2 L2 T2.
 /3 width=8 by tri_TC_star_ind/ qed-.
 
-lemma fpbs_ind_dx: ∀h,o,G2,L2,T2. ∀R:relation3 genv lenv term. R G2 L2 T2 →
-                   (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
-                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → R G1 L1 T1.
+lemma fpbs_ind_dx: ∀h,G2,L2,T2. ∀Q:relation3 genv lenv term. Q G2 L2 T2 →
+                   (∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≽[h] ❪G,L,T❫ → ❪G,L,T❫ ≥[h] ❪G2,L2,T2❫ → Q G L T → Q G1 L1 T1) →
+                   ∀G1,L1,T1. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ → Q G1 L1 T1.
 /3 width=8 by tri_TC_star_ind_dx/ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma fpbs_refl: ∀h,o. tri_reflexive … (fpbs h o).
+lemma fpbs_refl: ∀h. tri_reflexive … (fpbs h).
 /2 width=1 by tri_inj/ qed.
 
-lemma fpbq_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G2, L2, T2⦄ →
-                 ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma fpbq_fpbs: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽[h] ❪G2,L2,T2❫ →
+                 ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
 /2 width=1 by tri_inj/ qed.
 
-lemma fpbs_strap1: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
-                   ⦃G, L, T⦄ ≽[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma fpbs_strap1: ∀h,G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ≥[h] ❪G,L,T❫ →
+                   ❪G,L,T❫ ≽[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
 /2 width=5 by tri_step/ qed-.
 
-lemma fpbs_strap2: ∀h,o,G1,G,G2,L1,L,L2,T1,T,T2. ⦃G1, L1, T1⦄ ≽[h, o] ⦃G, L, T⦄ →
-                   ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
+lemma fpbs_strap2: ∀h,G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ≽[h] ❪G,L,T❫ →
+                   ❪G,L,T❫ ≥[h] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
 /2 width=5 by tri_TC_strap/ qed-.
 
-(* Basic_2A1: uses: lleq_fpbs *)
-lemma ffdeq_fpbs: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-/3 width=1 by fpbq_fpbs, fpbq_ffdeq/ qed.
+(* Basic_2A1: uses: lleq_fpbs fleq_fpbs *)
+lemma feqx_fpbs: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
+/3 width=1 by fpbq_fpbs, fpbq_feqx/ qed.
 
 (* Basic_2A1: uses: fpbs_lleq_trans *)
-lemma fpbs_ffdeq_trans: ∀h,o,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G, L, T⦄ →
-                        ∀G2,L2,T2. ⦃G, L, T⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-/3 width=9 by fpbs_strap1, fpbq_ffdeq/ qed-.
+lemma fpbs_feqx_trans: ∀h,G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥[h] ❪G,L,T❫ →
+                       ∀G2,L2,T2. ❪G,L,T❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
+/3 width=9 by fpbs_strap1, fpbq_feqx/ qed-.
 
 (* Basic_2A1: uses: lleq_fpbs_trans *)
-lemma ffdeq_fpbs_trans: ∀h,o,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ →
-                        ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≛[h, o] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
-/3 width=5 by fpbs_strap2, fpbq_ffdeq/ qed-.
+lemma feqx_fpbs_trans: ∀h,G,G2,L,L2,T,T2. ❪G,L,T❫ ≥[h] ❪G2,L2,T2❫ →
+                       ∀G1,L1,T1. ❪G1,L1,T1❫ ≛ ❪G,L,T❫ → ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
+/3 width=5 by fpbs_strap2, fpbq_feqx/ qed-.
+
+lemma teqx_reqx_lpx_fpbs: ∀h,T1,T2. T1 ≛ T2 → ∀L1,L0. L1 ≛[T2] L0 →
+                          ∀G,L2. ❪G,L0❫ ⊢ ⬈[h] L2 → ❪G,L1,T1❫ ≥[h] ❪G,L2,T2❫.
+/4 width=5 by feqx_fpbs, fpbs_strap1, fpbq_lpx, feqx_intro_dx/ qed.
 
 (* Basic_2A1: removed theorems 3:
               fpb_fpbsa_trans fpbs_fpbsa fpbsa_inv_fpbs