
theorem simp1:
for F being Field
for E being FieldExtension of F
for T1,T2,T3 being Subset of E
st FAdj(F,T1) = FAdj(F,T2) holds FAdj(F,T1\/T3) = FAdj(F,T2\/T3)
proof
let F be Field, E be FieldExtension of F, T1,T2,T3 be Subset of E;
assume AS: FAdj(F,T1) = FAdj(F,T2);
reconsider Ea = E as FieldExtension of FAdj(F,T1) by FIELD_4:7;
reconsider T3a = T3 as Subset of Ea;
reconsider Eb = E as FieldExtension of FAdj(F,T2) by FIELD_4:7;
reconsider T3b = T3 as Subset of Eb;
thus FAdj(F,T2\/T3) = FAdj(FAdj(F,T2),T3b) by FIELD_13:18
                   .= FAdj(F,T1\/T3) by AS,FIELD_13:18;
end;
