
theorem GauF04complex:
for a,b be Real, f be Function of REAL,REAL st
(b <> 0 & for x be Real holds f.x= exp(-(x-a)^2/(2*b^2)))
holds
f is FuzzySet of REAL
proof
 let a,b be Real;
 let f be Function of REAL,REAL;
 assume A1:b<>0;
 assume A2: for x be Real holds f.x= exp(-(x-a)^2/(2*b^2));
 for x be Real holds f.x= exp_R(-(x-a)^2/(2*b^2))
 proof
  let x be Real;
  f.x=exp(-(x-a)^2/(2*b^2)) by A2
   .=exp_R(-(x-a)^2/(2*b^2)) by SIN_COS:49;
  hence thesis;
 end;
 hence thesis by GauF04,A1;
end;
