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

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   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/computation/cpds.ma".
  16 include "basic_2/equivalence/cpcs_cpcs.ma".
  17 include "basic_2/equivalence/cpes.ma".
  18
  19 (* DECOMPOSED EXTENDED PARALLEL EQUIVALENCE FOR TERMS ***********************)
  20
  21 (* Advanced properties ******************************************************)
  22
  23 lemma cpds_cpes_dx: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, g] T2.
  24 #h #g #G #L #T1 #T2 * /3 width=7 by cpcs_cprs_dx, ex4_3_intro/
  25 qed.
  26
  27 (* Advanced inversion lemmas ************************************************)
  28
  29 lemma cpes_inv_abst2: ∀h,g,a,G,L,W1,T1,T. ⦃G, L⦄ ⊢ T •*⬌*[h, g] ⓛ{a}W1.T1 →
  30                       ∃∃W2,T2. ⦃G, L⦄ ⊢ T •*➡*[h, g] ⓛ{a}W2.T2 & ⦃G, L⦄ ⊢ ⓛ{a}W1.T1 ➡* ⓛ{a}W2.T2.
  31 #h #g #a #G #L #W1 #T1 #T * #T0 #l #l0 #Hl0 #Hl #HT0 #H
  32 elim (cpcs_inv_abst2 … H) -H /3 width=7 by ex4_3_intro, ex2_2_intro/
  33 qed-.