
theorem
for a,b be Real, f be FuzzySet of REAL st
(for x be Real holds f.x= exp(-(x-a)^2/(2*b^2)))
holds
f is normalized
proof
 let a,b be Real, f be FuzzySet of REAL;
 assume A2: for x be Real holds f.x= exp(-(x-a)^2/(2*b^2));
 ex x being Element of REAL st f . x = 1
 proof
  A6:a is Element of REAL by XREAL_0:def 1;
  take a;
   f.a = exp(-(a-a)^2/(2*b^2)) by A2
    .=1 by SIN_COS3:20;
  hence thesis by A6;
 end;
 hence thesis;
end;
