matita/matita/contribs/lambdadelta/basic_2/etc/scpes/scpes.etc

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  14
  15 include "basic_2/notation/relations/dpconvstar_8.ma".
  16 include "basic_2/computation/scpds.ma".
  17
  18 (* STRATIFIED DECOMPOSED PARALLEL EQUIVALENCE FOR TERMS *********************)
  19
  20 definition scpes: ∀h. sd h → nat → nat → relation4 genv lenv term term ≝
  21                   λh,o,d1,d2,G,L,T1,T2.
  22                   ∃∃T. ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d1] T & ⦃G, L⦄ ⊢ T2 •*➡*[h, o, d2] T.
  23
  24 interpretation "stratified decomposed parallel equivalence (term)"
  25    'DPConvStar h o d1 d2 G L T1 T2 = (scpes h o d1 d2 G L T1 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma scpds_div: ∀h,o,G,L,T1,T2,T,d1,d2.
  30                  ⦃G, L⦄ ⊢ T1 •*➡*[h, o, d1] T → ⦃G, L⦄ ⊢ T2 •*➡*[h, o, d2] T →
  31                  ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2.
  32 /2 width=3 by ex2_intro/ qed.
  33
  34 lemma scpes_sym: ∀h,o,G,L,T1,T2,d1,d2. ⦃G, L⦄ ⊢ T1 •*⬌*[h, o, d1, d2] T2 →
  35                  ⦃G, L⦄ ⊢ T2 •*⬌*[h, o, d2, d1] T1.
  36 #h #o #G #L #T1 #T2 #L1 #d2 * /2 width=3 by scpds_div/
  37 qed-.