Section PolyXY_ComRing.
Variable R : comRingType.
Implicit Types (u : {poly {poly R}}) (p : {poly R}) (x y : R).

Lemma sub_annihilantP p q x y :
p != 0 -> q != 0 -> p.[x] = 0 -> q.[y] = 0 ->
(sub_annihilant p q).[x - y] = 0.