matita/matita/contribs/lambdadelta/basic_2/conversion/cpc.ma

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  14
  15 include "basic_2/reduction/cpr.ma".
  16
  17 (* CONTEXT-SENSITIVE PARALLEL CONVERSION ON TERMS ***************************)
  18
  19 definition cpc: lenv → relation term ≝
  20    λL,T1,T2. L ⊢ T1 ➡ T2 ∨ L ⊢ T2 ➡ T1.
  21
  22 interpretation
  23    "context-sensitive parallel conversion (term)"
  24    'PConv L T1 T2 = (cpc L T1 T2).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma cpc_refl: ∀L. reflexive … (cpc L).
  29 /2 width=1/ qed.
  30
  31 lemma cpc_sym: ∀L. symmetric … (cpc L).
  32 #L #T1 #T2 * /2 width=1/
  33 qed.
  34
  35 (* Basic forward lemmas *****************************************************)
  36
  37 lemma cpc_fwd_cpr: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → ∃∃T. L ⊢ T1 ➡ T & L ⊢ T2 ➡ T.
  38 #L #T1 #T2 * /2 width=3/
  39 qed.