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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "basic_2/reducibility/cpr.ma".
17 (* CONTEXT-SENSITIVE PARALLEL CONVERSION ON TERMS ***************************)
19 definition cpc: lenv → relation term ≝
20 λL,T1,T2. L ⊢ T1 ➡ T2 ∨ L ⊢ T2 ➡ T1.
23 "context-sensitive parallel conversion (term)"
24 'PConv L T1 T2 = (cpc L T1 T2).
26 (* Basic properties *********************************************************)
28 lemma cpc_refl: ∀L,T. L ⊢ T ⬌ T.
31 lemma cpc_sym: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → L ⊢ T2 ⬌ T1.
32 #L #T1 #T2 * /2 width=1/
35 lemma cpc_cpr: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → ∃∃T. L ⊢ T1 ➡ T & L ⊢ T2 ➡ T.
36 #L #T1 #T2 * /2 width=3/