
theorem FAt:
for F being Field,
    E being FieldExtension of F
for T being Subset of E holds T is Subset of FAdj(F,T)
proof
let R be Field, S be FieldExtension of R; let T be Subset of S;
set P = FAdj(R,T);
now let o be object;
  assume A: o in T;
  then reconsider a = o as Element of S;
  for U be Subfield of S st R is Subfield of U & T is Subset of U
    holds o in U by A;
  then a in carrierFA(T);
  hence o in the carrier of P by dFA;
  end;
hence thesis by TARSKI:def 3;
end;
