Module OrderedClause <: OrderedType
with Definition t:=clause
with Definition compare:=compare_clause'.
Definition t := clause.
Definition eq : clause -> clause -> Prop := Logic.eq.
Definition compare := compare_clause'.
Definition mem_add (x: elt) (s: t) : option t :=
if mem x s then None else Some (add x s).

Lemma mem_add_spec:
forall x s, mem_add x s = if mem x s then None else Some (add x s).