- nnAuto: we catch TypeCheckerFailure generated at the end of

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / fpbg.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma
index 574c35e106c1cb87b101ab0f7df3c9be3f6e93f7..5c8a6bd20e3479e469ea1707e111d931724fff0d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma
@@ -13,49 +13,27 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/lazybtpredstarproper_8.ma".
-include "basic_2/reduction/fpbc.ma".
+include "basic_2/reduction/fpb.ma".
+include "basic_2/computation/fpbs.ma".
 
 (* "QRST" PROPER PARALLEL COMPUTATION FOR CLOSURES **************************)
 
 definition fpbg: ∀h. sd h → tri_relation genv lenv term ≝
-                 λh,g. tri_TC … (fpbc h g).
+                 λh,g,G1,L1,T1,G2,L2,T2.
+                 ∃∃G,L,T. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G, L, T⦄ & ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄.
 
 interpretation "'qrst' proper parallel computation (closure)"
    'LazyBTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (fpbg h g G1 L1 T1 G2 L2 T2).
 
 (* Basic properties *********************************************************)
 
-lemma fpbc_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G2, L2, T2⦄ →
-                 ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-/2 width=1 by tri_inj/ qed.
+lemma fpb_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
+                ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
+/2 width=5 by ex2_3_intro/ qed.
 
-lemma fpbg_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                   ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≻≡[h, g] ⦃G2, L2, T2⦄ →
-                   ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-/2 width=5 by tri_step/ qed.
-
-lemma fpbg_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
-                   ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ →
-                   ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-/2 width=5 by tri_TC_strap/ qed.
-
-lemma fpbu_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h,g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
-/3 width=1 by fpbu_fpbc, fpbc_fpbg/ qed.
-
-(* Basic eliminators ********************************************************)
-
-lemma fpbg_ind: ∀h,g,G1,L1,T1. ∀R:relation3 ….
-                (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
-                (∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≻≡[h, g] ⦃G2, L2, T2⦄ → R G L T → R G2 L2 T2) →
-                ∀G2,L2,T2. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2.
-#h #g #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
-@(tri_TC_ind … IH1 IH2 G2 L2 T2 H)
-qed-.
-
-lemma fpbg_ind_dx: ∀h,g,G2,L2,T2. ∀R:relation3 ….
-                   (∀G1,L1,T1. ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1) →
-                   (∀G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≻≡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ >≡[h, g] ⦃G2, L2, T2⦄ → R G L T → R G1 L1 T1) →
-                   ∀G1,L1,T1. ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1.
-#h #g #G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
-@(tri_TC_ind_dx … IH1 IH2 G1 L1 T1 H)
+lemma fpbg_fpbq_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
+                       ⦃G1, L1, T1⦄ >≡[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
+                       ⦃G1, L1, T1⦄ >≡[h, g] ⦃G2, L2, T2⦄.
+#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 *
+/3 width=9 by fpbs_strap1, ex2_3_intro/
 qed-.