matita/matita/contribs/lambda_delta/basic_2/conversion/lfpc.ma

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  14
  15 include "basic_2/reducibility/lfpr.ma".
  16
  17 (* FOCALIZED PARALLEL CONVERSION ON LOCAL ENVIRONMENTS **********************)
  18
  19 definition lfpc: relation lenv ≝
  20    λL1,L2. ⦃L1⦄ ➡ ⦃L2⦄ ∨ ⦃L2⦄ ➡ ⦃L1⦄.
  21
  22 interpretation
  23    "focalized parallel conversion (local environment)"
  24    'FocalizedPConv L1 L2 = (lfpc L1 L2).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma lfpc_refl: ∀L. ⦃L⦄ ⬌ ⦃L⦄.
  29 /2 width=1/ qed.
  30
  31 lemma lfpc_sym: ∀L1,L2. ⦃L1⦄ ⬌ ⦃L2⦄ → ⦃L2⦄ ⬌ ⦃L1⦄.
  32 #L1 #L2 * /2 width=1/
  33 qed.
  34
  35 lemma lfpc_lfpr: ∀L1,L2. ⦃L1⦄ ⬌ ⦃L2⦄ → ∃∃L. ⦃L1⦄ ➡ ⦃L⦄ & ⦃L2⦄ ➡ ⦃L⦄.
  36 #L1 #L2 * /2 width=3/
  37 qed.