matita/matita/contribs/lambdadelta/basic_2/etc/cpue/cpmue.etc

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  14
  15 include "basic_2/notation/relations/predevalstar_6.ma".
  16 include "basic_2/rt_transition/cnu.ma".
  17 include "basic_2/rt_computation/cpms.ma".
  18
  19 (* T-UNBOUND EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS ******************)
  20
  21 definition cpmue (h) (n) (G) (L): relation2 term term ≝
  22            λT1,T2. ∧∧ ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 & ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃T2⦄.
  23
  24 interpretation "t-unbound evaluation for t-bound context-sensitive parallel rt-transition (term)"
  25    'PRedEvalStar h n G L T1 T2 = (cpmue h n G L T1 T2).
  26
  27 definition R_cpmue (h) (G) (L) (T): predicate nat ≝
  28            λn. ∃U. ⦃G,L⦄ ⊢ T ➡*[h,n] 𝐍*⦃U⦄.
  29
  30 (* Basic properties *********************************************************)
  31
  32 lemma cpmue_intro (h) (n) (G) (L):
  33       ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄.
  34 /2 width=1 by conj/ qed.
  35
  36 (* Basic forward lemmas *****************************************************)
  37
  38 lemma cpmue_fwd_cpms (h) (n) (G) (L):
  39       ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2.
  40 #h #n #G #L #T1 #T2 * #HT12 #_ //
  41 qed-.