Notation "y .-support" := (support_for y)
(at level 2, format "y .-support") : fun_scope.
Section EqTheory.
Variables (aT : finType) (rT : eqType).
Notation fT := {ffun aT -> rT}.
Implicit Types (y : rT) (D : pred aT) (R : pred rT) (f : fT).

Lemma supportP y D g :
reflect (forall x, x \notin D -> g x = y) (y.-support g \subset D).