matita/matita/contribs/lambdadelta/static_2/syntax/teq.ma

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  14
  15 include "ground/notation/relations/ideq_2.ma".
  16 include "static_2/syntax/teqg.ma".
  17
  18 (* SYNTACTIC EQUIVALENCE ON TERMS *******************************************)
  19
  20 definition teq: relation term ≝
  21            teqg (pr_eq …).
  22
  23 interpretation
  24   "context-free syntactic equivalence (term)"
  25   'IdEq T1 T2 = (teq T1 T2).
  26
  27 (* Basic properties *********************************************************)
  28
  29 lemma teq_refl:
  30       reflexive … teq.
  31 /2 width=1 by teqg_refl/ qed.
  32
  33 lemma teq_sym:
  34       symmetric … teq.
  35 /2 width=1 by teqg_sym/ qed-.
  36
  37 (* Basic inversion lemmas ***************************************************)
  38
  39 lemma teq_inv_eq:
  40       ∀T1,T2. T1 ≡ T2 → T1 = T2.
  41 #T1 #T2 #H elim H -H //
  42 qed-.
  43
  44 (* Advanced forward lemmas **************************************************)
  45
  46 lemma teq_repl_1 (R:predicate …):
  47       ∀T1. R T1 → ∀T2. T1 ≡ T2 → R T2.
  48 #R #T1 #HT1 #T2 #HT12
  49 <(teq_inv_eq … HT12) -T2 //
  50 qed-.
  51
  52 lemma teq_sym_repl_1 (R:predicate …):
  53       ∀T1. R T1 → ∀T2. T2 ≡ T1 → R T2.
  54 #R #T1 #HT1 #T2 #HT12
  55 >(teq_inv_eq … HT12) -T2 //
  56 qed-.