matita/matita/contribs/lambdadelta/basic_2/reducibility/cfpr.ma

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  14
  15 include "basic_2/reducibility/cpr.ma".
  16 include "basic_2/reducibility/fpr.ma".
  17
  18 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON CLOSURES *************************)
  19
  20 definition cfpr: lenv → bi_relation lenv term ≝
  21                  λL,L1,T1,L2,T2. |L1| = |L2| ∧ L ⊢ L1 @@ T1 ➡ L2 @@ T2.
  22
  23 interpretation
  24    "context-sensitive parallel reduction (closure)"
  25    'FocalizedPRed L L1 T1 L2 T2 = (cfpr L L1 T1 L2 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma cfpr_refl: ∀L. bi_reflexive … (cfpr L).
  30 /2 width=1/ qed.
  31
  32 lemma fpr_cfpr: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ → ⋆ ⊢ ⦃L1, T1⦄ ➡ ⦃L2, T2⦄.
  33 #L1 #L2 #T1 #T2 * /3 width=1/
  34 qed.
  35
  36 (* Basic inversion lemmas ***************************************************)
  37
  38 lemma cfpr_inv_atom1: ∀L,L2,T1,T2. L ⊢ ⦃⋆, T1⦄ ➡ ⦃L2, T2⦄ → L ⊢ T1 ➡ T2 ∧ L2 = ⋆.
  39 #L #L2 #T1 #T2 * #H >(length_inv_zero_sn … H) /2 width=1/
  40 qed-.
  41
  42 (* Advanced inversion lemmas ************************************************)
  43
  44 lemma fpr_inv_pair1_sn: ∀I,K1,L2,V1,T1,T2. ⦃⋆.ⓑ{I}V1@@K1, T1⦄ ➡ ⦃L2, T2⦄ →
  45                         ∃∃K2,V2. V1 ➡ V2 &
  46                                  ⋆.ⓑ{I}V2 ⊢ ⦃K1, T1⦄ ➡ ⦃K2, T2⦄  &
  47                                  L2 = ⋆.ⓑ{I}V2@@K2.
  48 #I1 #K1 #L2 #V1 #T1 #T2 * >append_length #H
  49 elim (length_inv_pos_sn_append … H) -H #I2 #K2 #V2 #HK12 #H destruct
  50 >shift_append_assoc >shift_append_assoc normalize in ⊢ (%→?); #H
  51 elim (tpr_inv_bind1 … H) -H *
  52 [ #V0 #T #T0 #HV10 #HT1 #HT0 #H destruct /5 width=5/
  53 | #T0 #_ #_ #H destruct
  54 ]
  55 qed-.