
theorem
  for f,g be Function of REAL,REAL st
    f is continuous & g is continuous holds
    max(f,g) is continuous
proof
 let f,g be Function of REAL,REAL;
 assume A1: f is continuous;
 assume A2: g is continuous;
 for x be Real holds max(f,g).x = max(f.x, g.x)
 proof
  let x be Real;
  reconsider x as Element of REAL by XREAL_0:def 1;
  max(f,g).x = max(f.x, g.x) by COUSIN2:def 2;
  hence thesis;
 end;
 hence thesis by FUZZY_5:16,A1,A2;
end;
