
theorem diveq:
for F being Field,
    p being non zero Element of the carrier of Polynom-Ring F
for a being non zero Element of F
holds MonicDivisors p = MonicDivisors (a * p)
proof
let F be Field, p be non zero Element of the carrier of Polynom-Ring F;
let a be non zero Element of F;
A: now let o be object;
   assume o in MonicDivisors p; then
   consider q being monic Element of the carrier of Polynom-Ring F such that
   B: o = q & q divides p;
   q divides a * p by B,RING_5:15;
   hence o in MonicDivisors(a*p) by B;
   end;
now let o be object;
   assume o in MonicDivisors(a*p); then
   consider q being monic Element of the carrier of Polynom-Ring F such that
   B: o = q & q divides a * p;
   q divides p by B,RING_5:15;
   hence o in MonicDivisors p by B;
   end;
hence thesis by A,TARSKI:2;
end;
