theorem asymTT8: :: FUZZY_5:84

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