Notation "p ^:P" := (p ^ polyC) (at level 2, format "p ^:P") : ring_scope.Local Notation eval := horner_eval.Implicit Types (u : {poly {poly R}}) (p : {poly R}) (x y : R).Fact swapXY_key : unit.Definition swapXY := locked_with swapXY_key swapXY_def.

(* Specifications: *)
Lemma swapXY_is_additive : additive swapXY.