
theorem lemNor1cy:
for F1,F2 being Field
for p being Polynomial of F1 for a being Element of F1
for q being Polynomial of F2 for b being Element of F2
st F1 == F2 holds p = q & a = b implies a * p = b * q
proof
let F1,F2 be Field;
let p be Polynomial of F1; let a be Element of F1;
let q be Polynomial of F2; let b be Element of F2;
assume F1 == F2; then
   F1 is Subfield of F2 by FIELD_7:def 2; then
A: F2 is FieldExtension of F1 by FIELD_4:7;
assume p = q & a = b;
hence thesis by A,lemNor1cv;
end;
