matita/matita/contribs/lambdadelta/basic_2/static/steq.ma

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  14
  15 include "basic_2/notation/relations/lazyeq_4.ma".
  16 include "basic_2/grammar/term.ma".
  17 include "basic_2/static/sd.ma".
  18
  19 (* STRATIFIED EQUIVALENCE FOR TERMS *****************************************)
  20
  21 inductive steq (h) (g): relation term ≝
  22 | steq_refl: ∀T. steq h g T T
  23 | steq_zero: ∀k1,k2. deg h g k1 0 → deg h g k2 0 → steq h g (⋆k1) (⋆k2)
  24 .
  25
  26 interpretation
  27    "stratified equivalence (term)"
  28    'LazyEq h g T1 T2 = (steq h g T1 T2).
  29
  30 (* Basic inversion lemmas ****************************************************)
  31
  32 lemma steq_inv: ∀h,g,T1,T2. T1 ≡[h, g] T2 → T1 = T2 ∨
  33                 ∃∃k1,k2. deg h g k1 0 & deg h g k2 0 & T1 = ⋆k1 & T2 = ⋆k2.
  34 #h #g #T1 #T2 * /3 width=6 by or_introl, or_intror, ex4_2_intro/
  35 qed-.
  36
  37 (* Basic properties *********************************************************)
  38
  39 lemma steq_sym: ∀h,g. symmetric … (steq h g).
  40 #h #g #T1 #T2 * /2 width=1 by steq_zero/
  41 qed-.