proposition: Lemma size_MXnaddC (R : ringType) (p : {poly R}) (c : R) n : size (p * 'X^n.+1 + c%:P) = if (p == 0) then size c%:P else (n.+1 + size p)%N.
proof: Proof. have [->|/eqP hp0] := eqP; first by rewrite mul0r add0r. rewrite size_addl polyseqMXn ?size_ncons // size_polyC. by case: (c == 0)=> //=; rewrite ltnS ltn_addl // size_poly_gt0. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq zmodp) mathcomp(path choice fintype tuple finset ssralg bigop poly polydiv) CoqEAL(param refinements pos hrel poly_op)