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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
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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".
19 (* T-UNBOUND EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS ******************)
21 definition cpmue (h) (n) (G) (L): relation2 term term ≝
22 λT1,T2. ∧∧ ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 & ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃T2⦄.
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).
27 definition R_cpmue (h) (G) (L) (T): predicate nat ≝
28 λn. ∃U. ⦃G,L⦄ ⊢ T ➡*[h,n] 𝐍*⦃U⦄.
30 (* Basic properties *********************************************************)
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.
36 (* Basic forward lemmas *****************************************************)
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 #_ //