reserve A for non empty closed_interval Subset of REAL;

theorem Lm22B3:
for a,b,c,d be Real, f be Function of REAL,REAL st
b > 0 & c > 0 & d > 0 &
( for x be Real holds f.x = min(d, max(0, b - |. b*(x-a)/c .|)) )
holds (for x be Real st x in (A \ ['a-c,a+c']) holds f.x = 0)
proof
 let a,b,c,d be Real, f be Function of REAL,REAL;
 assume that
 A1: b > 0 & c > 0 and
 A2: d > 0 and
 A3: for x be Real holds f.x = min(d, max(0, b - |. b*(x-a)/c .|));
  let x be Real;
  assume A4: x in (A \ ['a-c,a+c']);
  not x in ['a-c,a+c'] by XBOOLE_0:def 5,A4;
  hence thesis by FU710,A1,A2,A3;
end;
