End UniqProperties.
(* *********************************************************************** *)
(** * Basic facts about [binds] *)
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_dom_contradiction : forall (E : list (atom*A)),
binds x a E ->
~ In x (dom E) ->
False.