Section BoolSpec.
Variable elt elt' elt'' : Type.
Implicit Types m : t elt.
Implicit Types x y z : key.
Implicit Types e : elt.
Hint Resolve add_neq_o : map.
Hint Resolve remove_eq_o : map.
Hint Resolve remove_neq_o : map.

Lemma remove_eq_b : forall m x y,
E.eq x y -> mem y (remove x m) = false.