theorem Th8:
  for SK1,SK2 be strict Subfield of K holds
  SK1 = SK2 iff the carrier of SK1 = the carrier of SK2
  proof
    let SK1, SK2 be strict Subfield of K;
    thus SK1 = SK2 implies
    the carrier of SK1 = the carrier of SK2;
    assume A1: the carrier of SK1 = the carrier of SK2;
    then A2: SK2 is strict Subfield of SK1 by Th6;
    SK1 is strict Subfield of SK2 by A1,Th6;
    hence thesis by A2,Th4;
  end;
