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

theorem CCounter:
  for F being FuzzySet of C holds
    Core F = F " {1}
  proof
    let F be FuzzySet of C;
    thus Core F c= F " {1}
    proof
      let x be object;
      assume x in Core F; then
      consider xx being Element of C such that
A1:   x = xx & F.xx = 1;
A2:   F.xx in {1} by TARSKI:def 1,A1;
      dom F = C by FUNCT_2:def 1;
      hence thesis by A1,FUNCT_1:def 7,A2;
    end;
    let x be object;
    assume
a1: x in F " {1}; then
A1: x in dom F & F.x in {1} by FUNCT_1:def 7;
    reconsider xx = x as Element of C by a1;
    F.xx = 1 by A1,TARSKI:def 1;
    hence thesis;
  end;
