
theorem
for f be Function of REAL,REAL, a,b be Real st
b>0 & for x be Real holds f.x = max(0,1-|.(x-a)/b.|)
holds f is continuous
proof
 let f be Function of REAL,REAL, a,b be Real;
 assume A2:b>0; then
 A4:a-b<a & a<a+b by XREAL_1:44,XREAL_1:29;
 assume A1: for x be Real holds f.x = max(0,1-|.(x-a)/b.|);
  f=TriangularFS (a-b,a,a+b)
 proof
   A6:dom f = REAL & REAL=dom TriangularFS (a-b,a,a+b) by FUNCT_2:def 1;
   for x being object st x in dom f holds
   f . x = TriangularFS (a-b,a,a+b) . x
   proof
    let x be object;
    assume x in dom f; then
    x in REAL by FUNCT_2:def 1; then
    reconsider x as Real;
    f.x=max(0,1-|.(x-a)/b.|) by A1;
    hence thesis by TR6,A2;
   end;
   hence thesis by FUNCT_1:2, A6;
  end;
 hence thesis by A4,FUZNUM_1:30;
end;
