
theorem mmu:
for F being Field
for E being F-finite FieldExtension of F
for a being Element of E holds deg MinPoly(a,F) divides deg(E,F)
proof
let F be Field, E be F-finite FieldExtension of F, a be Element of E;
set K = FAdj(F,{a});
reconsider E1 = E as K-finite F-extending FieldExtension of K
                                             by FIELD_4:7,FIELD_7:31;
deg(E1,F) = deg(E1,K) * deg(K,F) by FIELD_7:30
         .= deg(E1,K) * deg MinPoly(a,F) by FIELD_6:67;
hence thesis by INT_1:def 3;
end;
