reserve n for Nat;

theorem divi1:
for R being non degenerated comRing,
    q being Polynomial of R
for p being non zero Polynomial of R
for b being non zero Element of R st q divides p holds q divides (b*p)
proof
let F be non degenerated comRing, q be Polynomial of F;
let p be non zero Polynomial of F; let b be non zero Element of F;
assume q divides p;
then consider r being Polynomial of F such that
A: p = q *' r by RING_4:1;
b * (r *' q) = (b * r) *' q by HURWITZ:19;
hence q divides (b*p) by A,RING_4:1;
end;
