matita/matita/contribs/lambdadelta/basic_2A/etc/fpr/fpc.etc

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  14
  15 notation "hvbox( ⦃ term 46 L1 , break term 46 T1 ⦄ ⬌ break ⦃ term 46 L2 , break term 46 T2 ⦄ )"
  16    non associative with precedence 45
  17    for @{ 'FocalizedPConv $L1 $T1 $L2 $T2 }.
  18
  19 notation "hvbox( ⦃ term 46 L1 , break term 46 T1 ⦄ ⬌ ⬌ break ⦃ term 46 L2 , break term 46 T2 ⦄ )"
  20    non associative with precedence 45
  21    for @{ 'FocalizedPConvAlt $L1 $T1 $L2 $T2 }.
  22
  23 include "basic_2/reducibility/fpr.ma".
  24
  25 (* CONTEXT-FREE PARALLEL CONVERSION ON CLOSURES *****************************)
  26
  27 definition fpc: bi_relation lenv term ≝
  28    λL1,T1,L2,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ ∨ ⦃L2, T2⦄ ➡ ⦃L1, T1⦄.
  29
  30 interpretation
  31    "context-free parallel conversion (closure)"
  32    'FocalizedPConv L1 T1 L2 T2 = (fpc L1 T1 L2 T2).
  33
  34 (* Basic properties *********************************************************)
  35
  36 lemma fpc_refl: bi_reflexive … fpc.
  37 /2 width=1/ qed.
  38
  39 lemma fpc_sym: bi_symmetric … fpc.
  40 #L1 #L2 #T1 #T2 * /2 width=1/
  41 qed.
  42
  43 (* Basic forward lemmas *****************************************************)
  44
  45 lemma fpc_fwd_fpr: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌ ⦃L2, T2⦄ →
  46                    ∃∃L,T. ⦃L1, T1⦄ ➡ ⦃L, T⦄ & ⦃L2, T2⦄ ➡ ⦃L, T⦄.
  47 #L1 #L2 #T1 #T2 * /2 width=4/
  48 qed.