
theorem simp3:
for F being Field
for E being FieldExtension of F
for K being strict Field holds
K in IntermediateFields(E,F) iff (F is Subfield of K & K is Subfield of E)
proof
let F be Field, E be FieldExtension of F, K be strict Field;
now assume K in IntermediateFields(E,F);
  then consider K1 being strict Field such that
  A: K1 = K & F is Subfield of K1 & K1 is Subfield of E by defY;
  thus F is Subfield of K & K is Subfield of E by A;
  end;
hence thesis by defY;
end;
