matita/matita/contribs/lambdadelta/basic_2A/conversion/cpc.ma

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  14
  15 include "basic_2A/notation/relations/pconv_4.ma".
  16 include "basic_2A/reduction/cpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL CONVERSION ON TERMS ***************************)
  19
  20 definition cpc: relation4 genv lenv term term ≝
  21                 λG,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 ∨ ⦃G, L⦄ ⊢ T2 ➡ T1.
  22
  23 interpretation
  24    "context-sensitive parallel conversion (term)"
  25    'PConv G L T1 T2 = (cpc G L T1 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma cpc_refl: ∀G,L. reflexive … (cpc G L).
  30 /2 width=1 by or_intror/ qed.
  31
  32 lemma cpc_sym: ∀G,L. symmetric … (cpc L G).
  33 #G #L #T1 #T2 * /2 width=1 by or_introl, or_intror/
  34 qed-.
  35
  36 (* Basic forward lemmas *****************************************************)
  37
  38 lemma cpc_fwd_cpr: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ➡ T & ⦃G, L⦄ ⊢ T2 ➡ T.
  39 #G #L #T1 #T2 * /2 width=3 by ex2_intro/
  40 qed-.