matita/matita/contribs/lambdadelta/basic_2/computation/fpbg.ma

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  14
  15 include "basic_2/notation/relations/lazybtpredstarproper_8.ma".
  16 include "basic_2/computation/fpbc.ma".
  17
  18 (* GENEARAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES *************)
  19
  20 definition fpbg: ∀h. sd h → tri_relation genv lenv term ≝
  21                  λh,g. tri_TC … (fpbc h g).
  22
  23 interpretation "general 'big tree' proper parallel computation (closure)"
  24    'LazyBTPRedStarProper h g G1 L1 T1 G2 L2 T2 = (fpbg h g G1 L1 T1 G2 L2 T2).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma fpbc_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻⋕[h, g] ⦃G2, L2, T2⦄ →
  29                  ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  30 /2 width=1 by tri_inj/ qed.
  31
  32 lemma fpbg_strap1: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
  33                    ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≻⋕[h, g] ⦃G2, L2, T2⦄ →
  34                    ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  35 /2 width=5 by tri_step/ qed.
  36
  37 lemma fpbg_strap2: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
  38                    ⦃G1, L1, T1⦄ ≻⋕[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ >⋕[h, g] ⦃G2, L2, T2⦄ →
  39                    ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  40 /2 width=5 by tri_TC_strap/ qed.
  41
  42 (* Note: this is used in the closure proof *)
  43 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⦄.
  44 /4 width=1 by fpbc_fpbg, fpbu_fpbc, fpbu_fqup/ qed.
  45
  46 (* Basic eliminators ********************************************************)
  47
  48 lemma fpbg_ind: ∀h,g,G1,L1,T1. ∀R:relation3 ….
  49                 (∀G2,L2,T2. ⦃G1, L1, T1⦄ ≻⋕[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2) →
  50                 (∀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) →
  51                 ∀G2,L2,T2. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄ → R G2 L2 T2.
  52 #h #g #G1 #L1 #T1 #R #IH1 #IH2 #G2 #L2 #T2 #H
  53 @(tri_TC_ind … IH1 IH2 G2 L2 T2 H)
  54 qed-.
  55
  56 lemma fpbg_ind_dx: ∀h,g,G2,L2,T2. ∀R:relation3 ….
  57                    (∀G1,L1,T1. ⦃G1, L1, T1⦄ ≻⋕[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1) →
  58                    (∀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) →
  59                    ∀G1,L1,T1. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄ → R G1 L1 T1.
  60 #h #g #G2 #L2 #T2 #R #IH1 #IH2 #G1 #L1 #T1 #H
  61 @(tri_TC_ind_dx … IH1 IH2 G1 L1 T1 H)
  62 qed-.