Section BindsProperties.
Variable  A B   : Type.
Variables f     : A -> B.
Variables x y   : atom.
Variables a b   : A.
Variables E F G : list (atom*A).

Axiom binds_map_1 :
(forall a b, f a = f b -> a = b) ->
binds x (f a) (map f E) ->
binds x a E.