 reserve A for non empty Subset of REAL;
 reserve A for non empty closed_interval Subset of REAL;

theorem Lm20:
  for a,b,c be Real, f be Function of REAL,REAL st
  b > 0 & c > 0 &
  (for x be Real holds f.x = max(0,b-|. b*(x-a)/c .|))
    holds
  f is_integrable_on A & f | A is bounded
proof
 let a,b,c be Real, f be Function of REAL,REAL;
 assume that
 A1: b > 0 and
 A2: c > 0 and
 A3: for x be Real holds f.x = max(0, b - |. b*(x-a)/c .|);
 reconsider f as PartFunc of REAL,REAL;
 f is Lipschitzian by Th14,A3,A1,A2; then
 A6: f | A is continuous;
 dom f = REAL by FUNCT_2:def 1;
 hence thesis by INTEGRA5:11,INTEGRA5:10,A6;
end;
