made executable again

[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 827912dfa000fe5fd6728e228925703d3f6b6f55..441b4f080a0b177f0f2cdf4da89fc47140da8f45 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs.ma
@@ -14,74 +14,36 @@
 
 include "ground/lib/star.ma".
 include "basic_2/notation/relations/predsubtystar_6.ma".
-include "basic_2/rt_transition/fpbq.ma".
+include "basic_2/rt_transition/fpb.ma".
 
 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
 
 definition fpbs: tri_relation genv lenv term ≝
-           tri_TC … fpbq.
+           tri_TC … fpb.
 
 interpretation
   "parallel rst-computation (closure)"
   'PRedSubTyStar  G1 L1 T1 G2 L2 T2 = (fpbs G1 L1 T1 G2 L2 T2).
 
-(* Basic eliminators ********************************************************)
-
-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:
-      ∀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:
-      tri_reflexive … fpbs.
-/2 width=1 by tri_inj/ qed.
-
-lemma fpbq_fpbs:
-      ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫ →
-      ❪G1,L1,T1❫ ≥ ❪G2,L2,T2❫.
+(* Basic_2A1: uses: fpbq_fpbs *)
+lemma fpb_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:
-      â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG,L,Tâ\9d« →
-      â\9dªG,L,Tâ\9d« â\89½ â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d«.
+      â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G,L,Tâ\9d© →
+      â\9d¨G,L,Tâ\9d© â\89½ â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
 /2 width=5 by tri_step/ qed-.
 
 lemma fpbs_strap2:
-      â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â\9dªG1,L1,T1â\9d« â\89½ â\9dªG,L,Tâ\9d« →
-      â\9dªG,L,Tâ\9d« â\89¥ â\9dªG2,L2,T2â\9d« â\86\92 â\9dªG1,L1,T1â\9d« â\89¥ â\9dªG2,L2,T2â\9d«.
+      â\88\80G1,G,G2,L1,L,L2,T1,T,T2. â\9d¨G1,L1,T1â\9d© â\89½ â\9d¨G,L,Tâ\9d© →
+      â\9d¨G,L,Tâ\9d© â\89¥ â\9d¨G2,L2,T2â\9d© â\86\92 â\9d¨G1,L1,T1â\9d© â\89¥ â\9d¨G2,L2,T2â\9d©.
 /2 width=5 by tri_TC_strap/ qed-.
 
-(* Basic_2A1: uses: lleq_fpbs fleq_fpbs *)
-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:
-      ∀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:
-      ∀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:
-      ∀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:
               fpb_fpbsa_trans fpbs_fpbsa fpbsa_inv_fpbs
 *)