milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / fpbs.ma

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 f5c9176b0ba3acbf9b12455e4c3fb152aa393021..ab299482339967424a61655e70da74a9917089c5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
@@ -13,62 +13,62 @@
 (**************************************************************************)
 
 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. ∀Q:relation3 genv lenv term. Q 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⦄ → Q G L T → Q G2 L2 T2) →
-                ∀G2,L2,T2. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → Q 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. ∀Q:relation3 genv lenv term. Q 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⦄ → Q G L T → Q G1 L1 T1) →
-                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄ → Q 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 fleq_fpbs *)
-lemma fdeq_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 fdeq_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_fdeq/ qed.
 
 (* Basic_2A1: uses: fpbs_lleq_trans *)
-lemma fpbs_fdeq_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⦄.
+lemma fpbs_fdeq_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_fdeq/ qed-.
 
 (* Basic_2A1: uses: lleq_fpbs_trans *)
-lemma fdeq_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⦄.
+lemma fdeq_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_fdeq/ qed-.
 
-lemma tdeq_rdeq_lpx_fpbs: ∀h,o,T1,T2. T1 ≛[h, o] T2 → ∀L1,L0. L1 ≛[h, o, T2] L0 →
-                          ∀G,L2. ⦃G, L0⦄ ⊢ ⬈[h] L2 → ⦃G, L1, T1⦄ ≥[h, o] ⦃G, L2, T2⦄.
+lemma tdeq_rdeq_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 fdeq_fpbs, fpbs_strap1, fpbq_lpx, fdeq_intro_dx/ qed.
 
 (* Basic_2A1: removed theorems 3: