matita/matita/contribs/lambdadelta/basic_2/equivalence/fpcs_cpcs.ma

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   5 (*      ||T||                                                             *)
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  14
  15 include "basic_2/computation/fprs_cprs.ma".
  16 include "basic_2/equivalence/cpcs_cpcs.ma".
  17 include "basic_2/equivalence/fpcs_fpcs.ma".
  18
  19 (* CONTEXT-FREE PARALLEL EQUIVALENCE ON CLOSURES ****************************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma fpcs_shift: ∀I,L1,L2,V1,V2,T1,T2. ⦃L1.ⓑ{I}V1, T1⦄ ⬌* ⦃L2.ⓑ{I}V2, T2⦄ →
  24                      ⦃L1, -ⓑ{I}V1.T1⦄ ⬌* ⦃L2, -ⓑ{I}V2.T2⦄.
  25 #I #L1 #L2 #V1 #V2 #T1 #T2 #H12
  26 elim (fpcs_inv_fprs … H12) -H12 #L #T #H1 #H2
  27 elim (fprs_inv_pair1 … H1) -H1 #K1 #U1 #_ #HTU1 #H destruct
  28 elim (fprs_inv_pair1 … H2) -H2 #K2 #U2 #_ #HTU2 #H destruct /2 width=4/
  29 qed.
  30
  31 lemma fpcs_bind_minus: ∀I,L1,L2,V1,V2,T1,T2. ⦃L1, -ⓑ{I}V1.T1⦄ ⬌* ⦃L2, -ⓑ{I}V2.T2⦄ →
  32                        ∀b. ⦃L1, ⓑ{b,I}V1.T1⦄ ⬌* ⦃L2, ⓑ{b,I}V2.T2⦄.
  33 #I #L1 #L2 #V1 #V2 #T1 #T2 #H12 #b
  34 elim (fpcs_inv_fprs … H12) -H12 #L #T #H1 #H2
  35 elim (fprs_fwd_bind2_minus … H1 b) -H1 #W1 #U1 #HTU1 #H destruct
  36 elim (fprs_fwd_bind2_minus … H2 b) -H2 #W2 #U2 #HTU2 #H destruct /2 width=4/
  37 qed.
  38
  39 lemma fpcs_shift_full: ∀I,L1,L2,V1,V2,T1,T2. ⦃L1.ⓑ{I}V1, T1⦄ ⬌* ⦃L2.ⓑ{I}V2, T2⦄ →
  40                        ∀b. ⦃L1, ⓑ{b,I}V1.T1⦄ ⬌* ⦃L2, ⓑ{b,I}V2.T2⦄.
  41 /3 width=1/ qed.
  42
  43 (* Properties on context-sensitive parallel equivalence for terms ***********)
  44
  45 lemma cpcs_fpcs: ∀L,T1,T2. L ⊢ T1 ⬌* T2 → ⦃L, T1⦄ ⬌* ⦃L, T2⦄.
  46 #L #T1 #T2 #H
  47 elim (cpcs_inv_cprs … H) -H /3 width=4 by fprs_div, cprs_fprs/ (**) (* too slow without trace *)
  48 qed.
  49
  50 (* Inversion lemmas on context-sensitive parallel equivalence for terms *****)
  51
  52 lemma fpcs_inv_cpcs: ∀L,T1,T2. ⦃L, T1⦄ ⬌* ⦃L, T2⦄ → L ⊢ T1 ⬌* T2.
  53 #L #T1 #T2 #H
  54 elim (fpcs_inv_fprs … H) -H /3 width=4 by cprs_div, fprs_fwd_cprs/
  55 qed-.