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15 include "basic_2/reducibility/lfpr.ma".
17 (* FOCALIZED PARALLEL CONVERSION ON LOCAL ENVIRONMENTS **********************)
19 definition lfpc: relation lenv ≝
20 λL1,L2. ⦃L1⦄ ➡ ⦃L2⦄ ∨ ⦃L2⦄ ➡ ⦃L1⦄.
23 "focalized parallel conversion (local environment)"
24 'FocalizedPConv L1 L2 = (lfpc L1 L2).
26 (* Basic properties *********************************************************)
28 lemma lfpc_refl: ∀L. ⦃L⦄ ⬌ ⦃L⦄.
31 lemma lfpc_sym: ∀L1,L2. ⦃L1⦄ ⬌ ⦃L2⦄ → ⦃L2⦄ ⬌ ⦃L1⦄.
35 lemma lfpc_lfpr: ∀L1,L2. ⦃L1⦄ ⬌ ⦃L2⦄ → ∃∃L. ⦃L1⦄ ➡ ⦃L⦄ & ⦃L2⦄ ➡ ⦃L⦄.