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

theorem
  for F being FuzzySet of C holds
    Core F = 1-cut F
  proof
    let F be FuzzySet of C;
    1-cut F = F " ([. 1, 1 .]) by AlphaCut1
           .= F " {1} by XXREAL_1:17;
    hence thesis by CCounter;
  end;
