theorem asymTT7: :: FUZZY_5:79

for a, b, p, q being Real st a > 0 & p > 0 & (1 - b) / a < (1 - q) / (- p) holds
for x being Real holds (TrapezoidalFS (((- b) / a),((1 - b) / a),((1 - q) / (- p)),(q / p))) . x = max (0,(min (1,((((AffineMap (a,b)) | ].-infty,((q - b) / (a + p)).[) +* ((AffineMap ((- p),q)) | [.((q - b) / (a + p)),+infty.[)) . x))))