
theorem ZZ3z:
for F being Field
for p,q being Polynomial of F
for r being non zero Polynomial of F st r*'q divides r*'p holds q divides p
proof
let F be Field, p,q be Polynomial of F;
let r be non zero Polynomial of F;
assume r *' q divides r *' p; then
consider u being Polynomial of F such that
A: (r *' q) *' u = r *' p by RING_4:1;
r *' p = r *' (q *' u) by A,POLYNOM3:33;
hence q divides p by RING_4:1,RATFUNC1:7;
end;
