
theorem Th1:
  for X,A,B being set st A in Fin X & B c= A holds B in Fin X
proof
  let X,A,B be set such that
A1: A in Fin X and
A2: B c= A;
  A c= X by A1,FINSUB_1:def 5;
  then B c= X by A2;
  hence thesis by A1,A2,FINSUB_1:def 5;
end;
