theorem :: FUZZY_5:89

for a, b, p, q being Real
for f being FuzzySet of REAL st a > 0 & p > 0 & (1 - b) / a < (1 - q) / (- p) & ( for x being Real holds f . x = max (0,(min (1,((((AffineMap (a,b)) | ].-infty,((q - b) / (a + p)).[) +* ((AffineMap ((- p),q)) | [.((q - b) / (a + p)),+infty.[)) . x)))) ) holds
( f is trapezoidal & f is normalized )