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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "basic_2/notation/relations/predevalwstar_6.ma".
16 include "basic_2/rt_computation/cnuw.ma".
18 (* T-UNBOUND WHD EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS **************)
20 definition cpmuwe (h) (n) (G) (L): relation2 term term ≝
21 λT1,T2. ∧∧ ❨G,L❩ ⊢ T1 ➡*[h,n] T2 & ❨G,L❩ ⊢ ➡𝐍𝐖*[h] T2.
23 interpretation "t-unbound whd evaluation for t-bound context-sensitive parallel rt-transition (term)"
24 'PRedEvalWStar h n G L T1 T2 = (cpmuwe h n G L T1 T2).
26 definition R_cpmuwe (h) (G) (L) (T): predicate nat ≝
27 λn. ∃U. ❨G,L❩ ⊢ T ➡*𝐍𝐖*[h,n] U.
29 (* Basic properties *********************************************************)
31 lemma cpmuwe_intro (h) (n) (G) (L):
32 ∀T1,T2. ❨G,L❩ ⊢ T1 ➡*[h,n] T2 → ❨G,L❩ ⊢ ➡𝐍𝐖*[h] T2 → ❨G,L❩ ⊢ T1 ➡*𝐍𝐖*[h,n] T2.
33 /2 width=1 by conj/ qed.
35 (* Advanced properties ******************************************************)
37 lemma cpmuwe_sort (h) (n) (G) (L) (T):
38 ∀s. ❨G,L❩ ⊢ T ➡*[h,n] ⋆s → ❨G,L❩ ⊢ T ➡*𝐍𝐖*[h,n] ⋆s.
39 /3 width=5 by cnuw_sort, cpmuwe_intro/ qed.
41 lemma cpmuwe_ctop (h) (n) (G) (T):
42 ∀i. ❨G,⋆❩ ⊢ T ➡*[h,n] #i → ❨G,⋆❩ ⊢ T ➡*𝐍𝐖*[h,n] #i.
43 /3 width=5 by cnuw_ctop, cpmuwe_intro/ qed.
45 lemma cpmuwe_zero_unit (h) (n) (G) (L) (T):
46 ∀I. ❨G,L.ⓤ[I]❩ ⊢ T ➡*[h,n] #0 → ❨G,L.ⓤ[I]❩ ⊢ T ➡*𝐍𝐖*[h,n] #0.
47 /3 width=6 by cnuw_zero_unit, cpmuwe_intro/ qed.
49 lemma cpmuwe_gref (h) (n) (G) (L) (T):
50 ∀l. ❨G,L❩ ⊢ T ➡*[h,n] §l → ❨G,L❩ ⊢ T ➡*𝐍𝐖*[h,n] §l.
51 /3 width=5 by cnuw_gref, cpmuwe_intro/ qed.
53 (* Basic forward lemmas *****************************************************)
55 lemma cpmuwe_fwd_cpms (h) (n) (G) (L):
56 ∀T1,T2. ❨G,L❩ ⊢ T1 ➡*𝐍𝐖*[h,n] T2 → ❨G,L❩ ⊢ T1 ➡*[h,n] T2.
57 #h #n #G #L #T1 #T2 * #HT12 #_ //