
theorem ZZ7:
for F being Field
for p,q being non zero Polynomial of F
for a being Element of F holds multiplicity(p,a) <= multiplicity(p*'q,a)
proof
let F be Field, p,q be non zero Polynomial of F; let a be Element of F;
multiplicity(p*'q,a) = multiplicity(p,a) + multiplicity(q,a) by UPROOTS:55;
hence thesis by NAT_1:11;
end;
