X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Ffpbg.ma;h=b5c336e2474f9eb8ac35b470934526da2b3bf997;hb=e76eade57c0454a58b0d58e5484efe9af417847e;hp=cf46c84d102cb54b99cacda65865f51cab2d5997;hpb=2ce98dc56948742e1d27ca4a8b96a3501962d968;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma
index cf46c84d1..b5c336e24 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma
@@ -12,79 +12,51 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/btpredstarproper_8.ma".
-include "basic_2/reduction/fpbc.ma".
-include "basic_2/computation/fpbs.ma".
+include "basic_2/notation/relations/lazybtpredstarproper_8.ma".
+include "basic_2/computation/fpbc.ma".
 
-(* "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES **********************)
+(* GENEARAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES *************)
 
-inductive fpbg (h) (g) (G1) (L1) (T1): relation3 genv lenv term ≝
-| fpbg_inj : ∀G,G2,L,L2,T,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≻[h, g] ⦃G2, L2, T2⦄ →
-             fpbg h g G1 L1 T1 G2 L2 T2
-| fpbg_step: ∀G,L,L2,T. fpbg h g G1 L1 T1 G L T → ⦃G, L⦄ ⊢ ➡[h, g] L2 → fpbg h g G1 L1 T1 G L2 T
-.
+definition fpbg: ∀h. sd h → tri_relation genv lenv term ≝
+                 λh,g. tri_TC … (fpbc h g).
 
-interpretation "'big tree' proper parallel computation (closure)"
-   'BTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (fpbg h g G1 L1 T1 G2 L2 T2).
+interpretation "general 'big tree' proper parallel computation (closure)"
+   'LazyBTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (fpbg h g G1 L1 T1 G2 L2 T2).
 
-(* Basic forvard lemmas *****************************************************)
+(* Basic properties *********************************************************)
 
-lemma fpbg_fwd_fpbs: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄ →
-                     ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G2 -L2 -T2
-/3 width=5 by fpbs_strap1, fpbc_fwd_fpb, fpb_lpx/
-qed-.
+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.
 
-(* Basic properties *********************************************************)
+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 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⦄.
-/3 width=5 by fpbg_inj, fpbg_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 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⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2
-lapply (fpbg_fwd_fpbs … H1) #H0
-elim (fpb_fpbc_or_fpn … H2) -H2 [| * #HG2 #HL2 #HT2 destruct ]
-/2 width=5 by fpbg_inj, fpbg_step/
-qed-.
+(* Note: this is used in the closure proof *)
+lemma fqup_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
+/4 width=1 by fpbc_fpbg, fpbu_fpbc, fpbu_fqup/ 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⦄.
-#h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim H2 -G2 -L2 -T2
-/3 width=5 by fpbg_step, fpbg_inj, fpbs_strap2/
-qed-.
+(* Basic eliminators ********************************************************)
 
-lemma fpbg_fpbs_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 #HT1 #HT2 @(fpbs_ind … HT2) -G2 -L2 -T2
-/2 width=5 by fpbg_strap1/
+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 fpbs_fpbg_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ →
-                       ∀G2,L2,T2. ⦃G, L, T⦄ >[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G #L1 #L #T1 #T #HT1 @(fpbs_ind … HT1) -G -L -T
-/3 width=5 by fpbg_strap2/
+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)
 qed-.
-
-lemma fqup_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊃+ ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >[h, g] ⦃G2, L2, T2⦄.
-#h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … L2 T2 H) -G2 -L2 -T2
-/4 width=5 by fpbg_strap1, fpbc_fpbg, fpbc_fqu, fpb_fquq, fqu_fquq/
-qed.
-
-lemma cpxs_fpbg: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) →
-                 ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
-#h #g #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
-[ #H elim H //
-| #T #T2 #_ #HT2 #IHT1 #HT12
-  elim (term_eq_dec T1 T) #H destruct
-  [ -IHT1 /4 width=1/
-  | lapply (IHT1 … H) -IHT1 -H -HT12 #HT1
-    @(fpbg_strap1 … HT1) -HT1 /2 width=1 by fpb_cpx/
-  ]
-]
-qed.
-
-lemma cprs_fpbg: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → (T1 = T2 → ⊥) →
-                 ⦃G, L, T1⦄ >[h, g] ⦃G, L, T2⦄.
-/3 width=1 by cprs_cpxs, cpxs_fpbg/ qed.