
theorem mmv:
for F being Field,
    E being FieldExtension of F,
    K being E-extending FieldExtension of F
for a being F-algebraic Element of E,
    b being F-algebraic Element of K st a = b holds MinPoly(a,F) = MinPoly(b,F)
proof
let F be Field, E be FieldExtension of F,
    K be E-extending FieldExtension of F;
let a be F-algebraic Element of E, b be F-algebraic Element of K;
H: E is Subfield of K by FIELD_4:7;
assume a = b; then
Ext_eval(MinPoly(a,F),b) = Ext_eval(MinPoly(a,F),a) by FIELD_7:14
                        .= 0.E by FIELD_6:52
                        .= 0.K by H,EC_PF_1:def 1;
hence thesis by FIELD_6:52;
end;
