matita/matita/contribs/lambdadelta/basic_2/etc/csup/ysteps.etc

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  14
  15 notation "hvbox( h ⊢ break ⦃ L1, break T1 ⦄ • ⭃ * break [ g ] break ⦃ L2 , break T2 ⦄ )"
  16    non associative with precedence 45
  17    for @{ 'YPRedStepStar $h $g $L1 $T1 $L2 $T2 }.
  18
  19 include "basic_2/substitution/csup.ma".
  20 include "basic_2/computation/yprs.ma".
  21
  22 (* ITERATED STEP OF HYPER PARALLEL COMPUTATION ON CLOSURES ******************)
  23
  24 inductive ysteps (h) (g) (L1) (T1) (L2) (T2): Prop ≝
  25 | ysteps_intro: h ⊢ ⦃L1, T1⦄ •⥸*[g] ⦃L2, T2⦄ → (L1 = L2 → T1 = T2 → ⊥) →
  26                 ysteps h g L1 T1 L2 T2
  27 .
  28
  29 interpretation "iterated step of hyper parallel computation (closure)"
  30    'YPRedStepStar h g L1 T1 L2 T2 = (ysteps h g L1 T1 L2 T2).
  31
  32 (* Basic properties *********************************************************)
  33
  34 lemma ssta_ysteps: ∀h,g,L,T,U,l. ⦃h, L⦄ ⊢ T •[g, l + 1] U →
  35                    h ⊢ ⦃L, T⦄ •⭃*[g] ⦃L, U⦄.
  36 #h #g #L #T #U #l #HTU
  37 @ysteps_intro /3 width=2/ #_ #H destruct
  38 elim (ssta_inv_refl … HTU)
  39 qed.
  40
  41 lemma csup_ysteps: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ > ⦃L2, T2⦄ →
  42                    h ⊢ ⦃L1, T1⦄ •⭃*[g] ⦃L2, T2⦄.
  43 #h #g #L1 #L2 #T1 #T2 #H
  44 lapply (csup_fwd_cw … H) #H1
  45 @ysteps_intro /3 width=1/ -H #H2 #H3 destruct
  46 elim (lt_refl_false … H1)
  47 qed.