matita/matita/contribs/lambdadelta/basic_2A/multiple/fleq.ma

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  14
  15 include "basic_2A/notation/relations/lazyeq_7.ma".
  16 include "basic_2A/grammar/genv.ma".
  17 include "basic_2A/multiple/lleq.ma".
  18
  19 (* LAZY EQUIVALENCE FOR CLOSURES ********************************************)
  20
  21 inductive fleq (l) (G) (L1) (T): relation3 genv lenv term ≝
  22 | fleq_intro: ∀L2. L1 ≡[T, l] L2 → fleq l G L1 T G L2 T
  23 .
  24
  25 interpretation
  26    "lazy equivalence (closure)"
  27    'LazyEq l G1 L1 T1 G2 L2 T2 = (fleq l G1 L1 T1 G2 L2 T2).
  28
  29 (* Basic properties *********************************************************)
  30
  31 lemma fleq_refl: ∀l. tri_reflexive … (fleq l).
  32 /2 width=1 by fleq_intro/ qed.
  33
  34 lemma fleq_sym: ∀l. tri_symmetric … (fleq l).
  35 #l #G1 #L1 #T1 #G2 #L2 #T2 * /3 width=1 by fleq_intro, lleq_sym/
  36 qed-.
  37
  38 (* Basic inversion lemmas ***************************************************)
  39
  40 lemma fleq_inv_gen: ∀G1,G2,L1,L2,T1,T2,l. ⦃G1, L1, T1⦄ ≡[l] ⦃G2, L2, T2⦄ →
  41                     ∧∧ G1 = G2 & L1 ≡[T1, l] L2 & T1 = T2.
  42 #G1 #G2 #L1 #L2 #T1 #T2 #l * -G2 -L2 -T2 /2 width=1 by and3_intro/
  43 qed-.