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

theorem
  for F being FuzzySet of C st
    F is normalized holds height F = 1
  proof
    let F be FuzzySet of C;
    assume F is normalized; then
    consider x being Element of C such that
A1: F.x = 1;
    x in C; then
    x in dom F by FUNCT_2:def 1; then
A2: 1 <= height F by XXREAL_2:4,FUNCT_1:3,A1;
    height F <= 1 by HgtBnd;
    hence height F = 1 by A2,XXREAL_0:1;
  end;
