theorem asymTT5: :: FUZZY_5:82

for a, b, p, q, r, s being Real
for f being Function of REAL,REAL st a > 0 & p > 0 & ( for x being Real holds f . x = max (r,(min (s,((((AffineMap (a,b)) | ].-infty,((q - b) / (a + p)).[) +* ((AffineMap ((- p),q)) | [.((q - b) / (a + p)),+infty.[)) . x)))) ) holds
f is Lipschitzian