The Coq Proof Assistant

# Library Coq.setoid_ring.Ring

Require Import Bool.
Require Export Ring_theory.
Require Export Ring_base.
Require Export InitialRing.
Require Export Ring_tac.
Lemma BoolTheory :
ring_theory false true xorb andb xorb (fun b:bool => b) (eq(A:=bool)).
Definition bool_eq (b1 b2:bool) :=
if b1 then b2 else negb b2.
Lemma bool_eq_ok : forall b1 b2, bool_eq b1 b2 = true -> b1 = b2.
Ltac bool_cst t :=
let t := eval hnf in t in
match t with
true => constr:(true)
| false => constr:(false)
| _ => constr:(NotConstant)
end.
Add Ring bool_ring : BoolTheory (decidable bool_eq_ok, constants [bool_cst]).