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

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  14
  15 include "basic_2/notation/relations/pconv_5.ma".
  16 include "basic_2/rt_transition/cpm.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL R-CONVERSION FOR TERMS ************************)
  19
  20 definition cpc: sh → relation4 genv lenv term term ≝
  21                 λh,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 ∨ ⦃G, L⦄ ⊢ T2 ➡[h] T1.
  22
  23 interpretation
  24    "context-sensitive parallel r-conversion (term)"
  25    'PConv h G L T1 T2 = (cpc h G L T1 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma cpc_refl: ∀h,G,L. reflexive … (cpc h G L).
  30 /2 width=1 by or_intror/ qed.
  31
  32 lemma cpc_sym: ∀h,G,L. symmetric … (cpc h L G).
  33 #h #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: ∀h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌[h] T2 →
  39                    ∃∃T. ⦃G, L⦄ ⊢ T1 ➡[h] T & ⦃G, L⦄ ⊢ T2 ➡[h] T.
  40 #h #G #L #T1 #T2 * /2 width=3 by ex2_intro/
  41 qed-.