theorem :: FUZZY_8:35

for a, b, c, d being Real
for f being Function of REAL,REAL st b > 0 & c > 0 & d > 0 & d < b & ( for x being Real holds f . x = min (d,(max (0,(b - |.((b * (x - a)) / c).|)))) ) holds
f | [.(a - c),(a + c).] = (((AffineMap ((b / c),(b - ((a * b) / c)))) | [.(a - c),(a + ((d - b) / (b / c))).]) +* ((AffineMap (0,d)) | [.(a + ((d - b) / (b / c))),(a + ((b - d) / (b / c))).])) +* ((AffineMap ((- (b / c)),(b + ((a * b) / c)))) | [.(a + ((b - d) / (b / c))),(a + c).])