matita/matita/contribs/lambdadelta/basic_2A/equivalence/scpes_cpcs.ma

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  14
  15 include "basic_2A/computation/scpds_scpds.ma".
  16 include "basic_2A/equivalence/cpcs_cpcs.ma".
  17 include "basic_2A/equivalence/scpes.ma".
  18
  19 (* STRATIFIED DECOMPOSED PARALLEL EQUIVALENCE FOR TERMS *********************)
  20
  21 (* Inversion lemmas on parallel equivalence for terms ***********************)
  22
  23 lemma scpes_inv_lstas_eq: ∀h,g,G,L,T1,T2,d1,d2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, d1, d2] T2 →
  24                           ∀U1. ⦃G, L⦄ ⊢ T1 •*[h, d1] U1 →
  25                           ∀U2. ⦃G, L⦄ ⊢ T2 •*[h, d2] U2 → ⦃G, L⦄ ⊢ U1 ⬌* U2.
  26 #h #g #G #L #T1 #T2 #d1 #d2 * #T #HT1 #HT2 #U1 #HTU1 #U2 #HTU2
  27 /3 width=8 by scpds_inv_lstas_eq, cprs_div/
  28 qed-.
  29
  30 (* Properties on parallel equivalence for terms *****************************)
  31
  32 lemma cpcs_scpes: ∀h,g,G,L,T1,d11. ⦃G, L⦄ ⊢ T1 ▪[h, g] d11 →
  33                   ∀U1,d12. d12 ≤ d11 → ⦃G, L⦄ ⊢ T1 •*[h, d12] U1 →
  34                   ∀T2,d21. ⦃G, L⦄ ⊢ T2 ▪[h, g] d21 →
  35                   ∀U2,d22. d22 ≤ d21 → ⦃G, L⦄ ⊢ T2 •*[h, d22] U2 →
  36                   ⦃G, L⦄ ⊢ U1 ⬌* U2 → ⦃G, L⦄ ⊢ T1 •*⬌*[h, g, d12, d22] T2.
  37 #h #g #G #L #T1 #d11 #HT1 #U1 #d12 #Hd121 #HTU1 #T2 #d21 #HT2 #U2 #d22 #Hd221 #HTU2 #HU12
  38 elim (cpcs_inv_cprs … HU12) -HU12 /3 width=6 by scpds_div, ex4_2_intro/
  39 qed.