(* QuickChick Prelude *)
Set Warnings "-extraction-opaque-accessed,-extraction".
Set Warnings "-notation-overridden,-parsing".
Set Bullet Behavior "Strict Subproofs".
(* End prelude *)
Derive (Arbitrary, Show) for ascii.
Derive (Sized, CanonicalSized) for ascii.
Derive SizeMonotonic for ascii using genSascii.
Derive SizedMonotonic for ascii using genSascii.
Derive SizedCorrect for ascii using genSascii and SizeMonotonicascii.
Derive (Arbitrary, Show) for string.
Derive (Sized, CanonicalSized) for string.
Derive SizeMonotonic for string using genSstring.
Derive SizedMonotonic for string.
Derive SizedCorrect for string using genSstring and SizeMonotonicstring.
Inductive id : Type :=
| Id : string -> id.
Derive (Arbitrary, Show) for id.
Derive (Sized, CanonicalSized) for id.
Derive SizeMonotonic for id using genSid.
Derive SizedMonotonic for id.
Derive SizedCorrect for id using genSid and SizeMonotonicid.
Instance eq_dec_id (x y : id) : Dec (x = y).
constructor; unfold decidable. repeat decide equality. Defined.
Definition beq_id x y :=
match x,y with
| Id n1, Id n2 => if string_dec n1 n2 then true else false
end.
Admitted. (* QuickChick beq_id_refl. *)
Admitted. (* Prop *)

Theorem beq_id_false_iff : forall x y : id,
beq_id x y = false
<-> x <> y.