(* Instances of [ZifyClasses] for dealing with boolean operators. *)

#[global]
Instance Inj_bool_bool : InjTyp bool bool :=
  { inj b := b ; pred b := b = true \/ b = false ;
    cstr b := ltac:(destruct b; tauto) }.(** Boolean operators *)

#[global]
Instance Op_andb : BinOp andb :=
  { TBOp := andb ; TBOpInj _ _ := eq_refl}.#[global]
Instance Op_orb : BinOp orb :=
  { TBOp := orb ; TBOpInj _ _ := eq_refl}.#[global]
Instance Op_implb : BinOp implb :=
  { TBOp := implb; TBOpInj _ _ := eq_refl }.

(* Specifications: *)
Lemma xorb_eq b1 b2 : xorb b1 b2 = andb (orb b1 b2) (negb (eqb b1 b2)).