Module Dec2Bool (E:DecidableType) <: BooleanDecidableType
 := E <+ HasEqDec2Bool.Module Bool2Dec (E:BooleanEqualityType) <: BooleanDecidableType
 := E <+ HasEqBool2Dec.(** [eqb] is compatible with [eq] *)

#[global]
Instance eqb_compat : Proper (E.eq ==> E.eq ==> Logic.eq) eqb.

Lemma eqb_neq x y : (x =? y) = false <-> x ~= y.