matita/matita/contribs/lambda_delta/basic_2/reducibility/fpr.ma

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  14
  15 include "basic_2/reducibility/tpr.ma".
  16
  17 (* FOCALIZED PARALLEL REDUCTION ON CLOSURES *********************************)
  18
  19 definition fpr: bi_relation lenv term ≝
  20                 λL1,T1,L2,T2. |L1| = |L2| ∧ L1 @@ T1 ➡ L2 @@ T2.
  21
  22 interpretation
  23    "focalized parallel reduction (closure)"
  24    'FocalizedPRed L1 T1 L2 T2 = (fpr L1 T1 L2 T2).
  25
  26 (* Basic properties *********************************************************)
  27
  28 lemma fpr_refl: bi_reflexive … fpr.
  29 /2 width=1/ qed.
  30
  31 (* Basic inversion lemmas ***************************************************)
  32
  33 lemma fpr_inv_atom1: ∀L2,T1,T2. ⦃⋆, T1⦄ ➡ ⦃L2, T2⦄ → T1 ➡ T2 ∧ L2 = ⋆.
  34 #L2 #T1 #T2 * #H
  35 lapply (length_inv_zero_sn … H) -H #H destruct /2 width=1/
  36 qed-.
  37 (*
  38 lemma fpr_inv_pair1: ∀I,K1,L2,V1,T1,T2. ⦃K1.ⓑ{I}V1, T1⦄ ➡ ⦃L2, T2⦄ →
  39                      ∃∃K2,V2. ⦃K1, -ⓑ{I}V1.T1⦄ ➡ ⦃K2, -ⓑ{I}V2.T2⦄  &
  40                               L2 = K2.ⓑ{I}V2.
  41 #I1 #K1 #L2 #V1 #T1 #T2 * #H
  42 elim (length_inv_pos_sn … H) -H #I2 #K2 #V2 #HK12 #H destruct #H
  43 elim (tpr_fwd_shift_bind_minus … H) // #_ #H0 destruct /3 width=4/
  44 qed-.
  45 *)
  46 lemma fpr_inv_atom3: ∀L1,T1,T2. ⦃L1,T1⦄ ➡ ⦃⋆,T2⦄ → T1 ➡ T2 ∧ L1 = ⋆.
  47 #L1 #T1 #T2 * #H
  48 lapply (length_inv_zero_dx … H) -H #H destruct /2 width=1/
  49 qed-.
  50 (*
  51 lemma fpr_inv_pair3: ∀I,L1,K2,V2,T1,T2. ⦃L1, T1⦄ ➡ ⦃K2.ⓑ{I}V2, T2⦄ →
  52                      ∃∃K1,V1. ⦃K1, -ⓑ{I}V1.T1⦄ ➡ ⦃K2, -ⓑ{I}V2.T2⦄  &
  53                               L1 = K1.ⓑ{I}V1.
  54 #I2 #L1 #K2 #V2 #T1 #T2 * #H
  55 elim (length_inv_pos_dx … H) -H #I1 #K1 #V1 #HK12 #H destruct #H
  56 elim (tpr_fwd_shift_bind_minus … H) // #_ #H0 destruct /3 width=4/
  57 qed-.
  58 *)