milestone update in basic_2, update in ground and static_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 a945cf34c132c564eebb503c1cbd06fd3b739664..827912dfa000fe5fd6728e228925703d3f6b6f55 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 +13,73 @@
 (**************************************************************************)
 
 include "ground/lib/star.ma".
-include "basic_2/notation/relations/predsubtystar_7.ma".
+include "basic_2/notation/relations/predsubtystar_6.ma".
 include "basic_2/rt_transition/fpbq.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
 
-definition fpbs: ∀h. tri_relation genv lenv term ≝
-                 λh. tri_TC … (fpbq h).
+definition fpbs: tri_relation genv lenv term ≝
+           tri_TC … fpbq.
 
-interpretation "parallel rst-computation (closure)"
-   'PRedSubTyStar  h G1 L1 T1 G2 L2 T2 = (fpbs h G1 L1 T1 G2 L2 T2).
+interpretation
+  "parallel rst-computation (closure)"
+  'PRedSubTyStar  G1 L1 T1 G2 L2 T2 = (fpbs G1 L1 T1 G2 L2 T2).
 
 (* Basic eliminators ********************************************************)
 
-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.
+lemma fpbs_ind:
+      ∀G1,L1,T1. ∀Q:relation3 genv lenv term. Q G1 L1 T1 →
+      (∀G,G2,L,L2,T,T2. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ → ❪G,L,T❫ ≽ ❪G2,L2,T2❫ → Q G L T → Q G2 L2 T2) →
+      ∀G2,L2,T2. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ → Q G2 L2 T2.
 /3 width=8 by tri_TC_star_ind/ qed-.
 
-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.
+lemma fpbs_ind_dx:
+      ∀G2,L2,T2. ∀Q:relation3 genv lenv term. Q G2 L2 T2 →
+      (∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≽ ❪G,L,T❫ → ❪G,L,T❫ ≥ ❪G2,L2,T2❫ → Q G L T → Q G1 L1 T1) →
+      ∀G1,L1,T1. ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫ → Q G1 L1 T1.
 /3 width=8 by tri_TC_star_ind_dx/ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma fpbs_refl: ∀h. tri_reflexive … (fpbs h).
+lemma fpbs_refl:
+      tri_reflexive … fpbs.
 /2 width=1 by tri_inj/ qed.
 
-lemma fpbq_fpbs: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽[h] ❪G2,L2,T2❫ →
-                 ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫.
+lemma fpbq_fpbs:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
+      ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /2 width=1 by tri_inj/ qed.
 
-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❫.
+lemma fpbs_strap1:
+      ∀G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
+      ❪G,L,T❫ ≽ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /2 width=5 by tri_step/ qed-.
 
-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❫.
+lemma fpbs_strap2:
+      ∀G1,G,G2,L1,L,L2,T1,T,T2. ❪G1,L1,T1❫ ≽ ❪G,L,T❫ →
+      ❪G,L,T❫ ≥ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /2 width=5 by tri_TC_strap/ 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❫.
+lemma feqx_fpbs:
+      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /3 width=1 by fpbq_fpbs, fpbq_feqx/ qed.
 
 (* Basic_2A1: uses: fpbs_lleq_trans *)
-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❫.
+lemma fpbs_feqx_trans:
+      ∀G1,G,L1,L,T1,T. ❪G1,L1,T1❫ ≥ ❪G,L,T❫ →
+      ∀G2,L2,T2. ❪G,L,T❫ ≛ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
 /3 width=9 by fpbs_strap1, fpbq_feqx/ qed-.
 
 (* Basic_2A1: uses: lleq_fpbs_trans *)
-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❫.
+lemma feqx_fpbs_trans:
+      ∀G,G2,L,L2,T,T2. ❪G,L,T❫ ≥ ❪G2,L2,T2❫ →
+      ∀G1,L1,T1. ❪G1,L1,T1❫ ≛ ❪G,L,T❫ → ❪G1,L1,T1❫ ≥ ❪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❫.
+lemma teqx_reqx_lpx_fpbs:
+      ∀T1,T2. T1 ≛ T2 → ∀L1,L0. L1 ≛[T2] L0 →
+      ∀G,L2. ❪G,L0❫ ⊢ ⬈ L2 → ❪G,L1,T1❫ ≥ ❪G,L2,T2❫.
 /4 width=5 by feqx_fpbs, fpbs_strap1, fpbq_lpx, feqx_intro_dx/ qed.
 
 (* Basic_2A1: removed theorems 3: