theorem Th24: :: FUZZY_9:25

for A being non empty closed_interval Subset of REAL
for p, q, r, s, t, u being Real
for f being Function of REAL,REAL st p * s < 0 & p > 0 & ( for x being Real holds f . x = max (r,(min (u,((((AffineMap (p,q)) | ].-infty,((t - q) / (p - s)).]) +* ((AffineMap (s,t)) | [.((t - q) / (p - s)),+infty.[)) . x)))) ) holds
f is Lipschitzian