
theorem lemNor3xx:
for F being Field,
    E,K being FieldExtension of F,
    U1 being FieldExtension of E, U2 being FieldExtension of K
for T1 being Subset of U1, T2 being Subset of U2
st U1 = U2 & T1 = T2 & E == K holds FAdj(E,T1) = FAdj(K,T2)
proof
let F be Field, E,K be FieldExtension of F;
let U1 be FieldExtension of E, U2 be FieldExtension of K;
let T1 be Subset of U1, T2 be Subset of U2;
assume AS: U1 = U2 & T1 = T2 & E == K;
A: FAdj(E,T1) is Subfield of FAdj(K,T2)
   proof
   FAdj(K,T2) is FieldExtension of E by AS,FIELD_12:37; then
   A1: E is Subfield of FAdj(K,T2) by FIELD_4:7;
   T1 is Subset of FAdj(K,T2) by AS,FIELD_6:35;
   hence thesis by AS,A1,FIELD_6:37;
   end;
FAdj(K,T2) is Subfield of FAdj(E,T1)
   proof
   FAdj(E,T1) is FieldExtension of K by AS,FIELD_12:37; then
   A1: K is Subfield of FAdj(E,T1) by FIELD_4:7;
   T2 is Subset of FAdj(E,T1) by AS,FIELD_6:35;
   hence thesis by AS,A1,FIELD_6:37;
   end;
hence thesis by A,EC_PF_1:4;
end;
