
theorem ClA:
for F being Field holds
F is algebraic-closed iff
for E being F-algebraic FieldExtension of F holds E == F
proof
let F be Field;
A: now assume F is algebraic-closed;
   then F is maximal_algebraic by eq;
   hence for E being F-algebraic FieldExtension of F holds E == F;
   end;
now assume for E being F-algebraic FieldExtension of F holds E == F;
  then F is maximal_algebraic;
  hence F is algebraic-closed by eq;
  end;
hence thesis by A;
end;
