End BindsProperties.
Section BindsProperties2.
Variable  A B   : Type.
Variables f     : A -> B.
Variables x y   : X.t.
Variables a b   : A.
Variables E F G : list (X.t*A).

Lemma binds_cons_uniq_iff :
uniq ((y, b) :: E) ->
(binds x a ((y, b) :: E) <->
(x = y /\ a = b /\ ~ In x (dom E)) \/
(binds x a E /\ x <> y)).