 reserve a,b,c,x for Real;
 reserve C for non empty set;

theorem
  Core UMF C = C
  proof
    thus Core UMF C c= C;
    let x be object;
    assume x in C; then
    reconsider xx = x as Element of C;
    (UMF C).xx = 1 by FUNCT_3:def 3;
    hence thesis;
  end;
