
theorem ZZ3y:
for F being Field
for p being monic Polynomial of F
for r being Polynomial of F st p *' r is monic holds r is monic
proof
let F be Field, p be monic Polynomial of F; let r be Polynomial of F;
assume p *' r is monic; then
1.F = LC(p *' r) by RATFUNC1:def 7
   .= LC(p) * LC(r) by NIVEN:46
   .= 1.F * LC(r) by RATFUNC1:def 7;
hence thesis by RATFUNC1:def 7;
end;
