
theorem Th14y:
for F being Field
for m being Ordinal st m in card(nonConstantPolys F)
for p being Polynomial of F holds
Poly(m,LM p) = Monom(LC Poly(m,p),Lt Poly(m,p))
proof
let F be Field, m be Ordinal;
assume AS: m in card(nonConstantPolys F);
let p be Polynomial of F;
set n = card(nonConstantPolys F), q = Poly(m,LM p);
thus Poly(m,LM p) = Monom(coefficient(q),term(q)) by POLYNOM7:11
            .= Monom(LC q,term(q)) by Th14x
            .= Monom(LC q,Lt q) by Th14x
            .= Monom(LC Poly(m,p),Lt q) by AS,Th14z
            .= Monom(LC Poly(m,p),Lt Poly(m,p)) by AS,Th14z;
end;
