reserve A for non empty closed_interval Subset of REAL;

theorem Lm22a:
for a,b,c,d be Real, f be Function of REAL,REAL st
c > 0 & ( for x be Real holds f.x = min(d, max(0, b - |. b*(x-a)/c .|)) )
holds f is_integrable_on A & f | A is bounded
proof
 let a,b,c,d be Real, f be Function of REAL,REAL;
 assume that
 A2:  c > 0 and
 A3: for x be Real holds f.x = min(d, max(0, b - |. b*(x-a)/c .|));
 reconsider f as PartFunc of REAL,REAL;
 f is Lipschitzian by L724,A2,A3; then
 A6: f | A is continuous;
 dom f = REAL by FUNCT_2:def 1;
 hence thesis by INTEGRA5:11,INTEGRA5:10,A6;
end;
