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15 include "basic_2/reducibility/lcpr.ma".
17 (* CONTEXT-SENSITIVE PARALLEL CONVERSION ON LOCAL ENVIRONMENTS **************)
19 definition lcpc: relation lenv ≝
20 λL1,L2. L1 ⊢ ➡ L2 ∨ L2 ⊢ ➡ L1.
23 "context-sensitive parallel conversion (local environment)"
24 'CPConv L1 L2 = (lcpc L1 L2).
26 (* Basic properties *********************************************************)
28 lemma lcpc_refl: ∀L. L ⊢ ⬌ L.
31 lemma lcpc_sym: ∀L1,L2. L1 ⊢ ⬌ L2 → L2 ⊢ ⬌ L1.
35 lemma lcpc_lcpr: ∀L1,L2. L1 ⊢ ⬌ L2 → ∃∃L. L1 ⊢ ➡ L & L2 ⊢ ➡ L.