matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpn/bteq.etc

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  14
  15 include "basic_2/notation/relations/bteq_6.ma".
  16 include "basic_2/grammar/lenv_length.ma".
  17 include "basic_2/grammar/genv.ma".
  18
  19 (* EQUIVALENT "BIG TREE" NORMAL FORMS ***************************************)
  20
  21 definition bteq: tri_relation genv lenv term ≝
  22                  λG1,L1,T1,G2,L2,T2.
  23                  ∧∧ G1 = G2 & |L1| = |L2| & T1 = T2.
  24
  25 interpretation
  26    "equivalent 'big tree' normal forms (closure)"
  27    'BTEq G1 L1 T1 G2 L2 T2 = (bteq G1 L1 T1 G2 L2 T2).
  28
  29 (* Basic_properties *********************************************************)
  30
  31 lemma bteq_refl: tri_reflexive … bteq.
  32 /2 width=1 by and3_intro/ qed.
  33
  34 lemma bteq_sym: tri_symmetric … bteq.
  35 #G1 #G2 #L1 #L2 #T1 #T2 * //
  36 qed-.
  37
  38 lemma bteq_dec: ∀G1,G2,L1,L2,T1,T2. Decidable (⦃G1, L1, T1⦄ ⋕ ⦃G2, L2, T2⦄).
  39 #G1 #G2 #L1 #L2 #T1 #T2 elim (genv_eq_dec G1 G2)
  40 #H1G [2: @or_intror * #H2G #H2L #H2T destruct /2 width=1 by/ ]
  41 elim (eq_nat_dec (|L1|) (|L2|))
  42 #H1L [2: @or_intror * #H2G #H2L #H2T destruct /2 width=1 by/ ]
  43 elim (term_eq_dec T1 T2)
  44 #H1T [2: @or_intror * #H2G #H2L #H2T destruct /2 width=1 by/ ]
  45 /3 width=1 by and3_intro, or_introl/
  46 qed-.