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

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  14
  15 include "basic_2/reducibility/lcpr.ma".
  16
  17 (* CONTEXT-SENSITIVE PARALLEL CONVERSION ON LOCAL ENVIRONMENTS **************)
  18
  19 definition lcpc: relation lenv ≝
  20    λL1,L2. L1 ⊢ ➡ L2 ∨ L2 ⊢ ➡ L1.
  21
  22 interpretation
  23    "context-sensitive parallel conversion (local environment)"
  24    'CPConv L1 L2 = (lcpc L1 L2).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma lcpc_refl: ∀L. L ⊢ ⬌ L.
  29 /2 width=1/ qed.
  30
  31 lemma lcpc_sym: ∀L1,L2. L1 ⊢ ⬌ L2 → L2 ⊢ ⬌ L1.
  32 #L1 #L2 * /2 width=1/
  33 qed.
  34
  35 lemma lcpc_lcpr: ∀L1,L2. L1 ⊢ ⬌ L2 → ∃∃L. L1 ⊢ ➡ L & L2 ⊢ ➡ L.
  36 #L1 #L2 * /2 width=3/
  37 qed.