
theorem multi2:
for F being Field,
    p being non zero Polynomial of F
for a being Element of F
for n being Element of NAT holds
n = multiplicity(p,a) iff ((X-a)`^n divides p & not (X-a)`^(n+1) divides p)
proof
let F be Field, p be non zero Polynomial of F;
let a be Element of F; let n be Element of NAT;
rpoly(1,a) = X-a by FIELD_9:def 2;
hence thesis by RING_5:33;
end;
