matita/matita/contribs/lambda_delta/basic_2/computation/yprs.ma

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  14
  15 include "basic_2/reducibility/ypr.ma".
  16
  17 (* HYPER PARALLEL COMPUTATION ON CLOSURES ***********************************)
  18
  19 definition yprs: ∀h. sd h → bi_relation lenv term ≝
  20                  λh,g. bi_TC … (ypr h g).
  21
  22 interpretation "hyper parallel computation (closure)"
  23    'YPRedStar h g L1 T1 L2 T2 = (yprs h g L1 T1 L2 T2).
  24
  25 (* Basic eliminators ********************************************************)
  26
  27 lemma yprs_ind: ∀h,g,L1,T1. ∀R:relation2 lenv term. R L1 T1 →
  28                 (∀L,L2,T,T2. h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ •⥸[g] ⦃L2, T2⦄ → R L T → R L2 T2) →
  29                 ∀L2,T2. h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄ → R L2 T2.
  30 /3 width=7 by bi_TC_star_ind/ qed-.
  31
  32 lemma yprs_ind_dx: ∀h,g,L2,T2. ∀R:relation2 lenv term. R L2 T2 →
  33                    (∀L1,L,T1,T. h ⊢ ⦃L1, T1⦄ •⥸[g] ⦃L, T⦄ → h ⊢ ⦃L, T⦄ •⥸*[g] ⦃L2, T2⦄ → R L T → R L1 T1) →
  34                    ∀L1,T1. h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄ → R L1 T1.
  35 /3 width=7 by bi_TC_star_ind_dx/ qed-.
  36
  37 (* Basic properties *********************************************************)
  38
  39 lemma yprs_refl: ∀h,g. bi_reflexive … (yprs h g).
  40 /2 width=1/ qed.
  41
  42 lemma yprs_strap1: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L, T⦄ →
  43                    h ⊢ ⦃L, T⦄ •⥸[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄.
  44 /2 width=4/ qed.
  45
  46 lemma yprs_strap2: ∀h,g,L1,L,L2,T1,T,T2. h ⊢ ⦃L1, T1⦄ •⥸[g] ⦃L, T⦄ →
  47                    h ⊢ ⦃L, T⦄ •⥸*[g] ⦃L2, T2⦄ → h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄.
  48 /2 width=4/ qed.