matita/matita/contribs/lambdadelta/basic_2/relocation/freq.ma

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  14
  15 include "basic_2/notation/relations/lazyeq_6.ma".
  16 include "basic_2/grammar/genv.ma".
  17 include "basic_2/relocation/frees_weight.ma".
  18 include "basic_2/relocation/frees_lreq.ma".
  19
  20 (* LAZY EQUIVALENCE FOR CLOSURES ********************************************)
  21
  22 inductive freq (G) (L1) (T): relation3 genv lenv term ≝
  23 | fleq_intro: ∀L2,f. L1 ⊢ 𝐅*⦃T⦄ ≡ f → L1 ≡[f] L2 → freq G L1 T G L2 T
  24 .
  25
  26 interpretation
  27    "ranged equivalence (closure)"
  28    'LazyEq G1 L1 T1 G2 L2 T2 = (freq G1 L1 T1 G2 L2 T2).
  29
  30 (* Basic properties *********************************************************)
  31
  32 lemma freq_refl: tri_reflexive … freq.
  33 #G #L #T elim (frees_total L T) /2 width=3 by fleq_intro/
  34 qed.
  35
  36 lemma freq_sym: tri_symmetric … freq.
  37 #G1 #L1 #T1 #G2 #L2 #T2 * /4 width=3 by fleq_intro, frees_lreq_conf, lreq_sym/
  38 qed-.
  39
  40 (* Basic inversion lemmas ***************************************************)
  41
  42 lemma freq_inv_gen: ∀G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≡ ⦃G2, L2, T2⦄ →
  43                     ∃∃f. G1 = G2 & L1 ⊢ 𝐅*⦃T1⦄ ≡ f & L1 ≡[f] L2 & T1 = T2.
  44 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=3 by ex4_intro/
  45 qed-.
  46
  47 (* Basic_2A1: removed theorems 6:
  48               fleq_refl fleq_sym fleq_inv_gen
  49               fleq_trans fleq_canc_sn fleq_canc_dx
  50 *)