let F1, F2 be Field; :: thesis: 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 & p = q & a = b holds
a * p = b * q
let p be Polynomial of F1; :: thesis: for a being Element of F1
for q being Polynomial of F2
for b being Element of F2 st F1 == F2 & p = q & a = b holds
a * p = b * q
let a be Element of F1; :: thesis: for q being Polynomial of F2
for b being Element of F2 st F1 == F2 & p = q & a = b holds
a * p = b * q
let q be Polynomial of F2; :: thesis: for b being Element of F2 st F1 == F2 & p = q & a = b holds
a * p = b * q
let b be Element of F2; :: thesis: ( F1 == F2 & p = q & a = b implies a * p = b * q )
assume F1 == F2 ; :: thesis: ( not p = q or not a = b or a * p = b * q )
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 ) ; :: thesis: a * p = b * q
hence a * p = b * q by A, lemNor1cv; :: thesis: verum