theorem :: FUZZY_8:33

for A being non empty closed_interval Subset of REAL
for a, b, c, d being Real
for f being Function of REAL,REAL st b > 0 & c > 0 & d > 0 & ['(a - c),(a + c)'] c= A & d < b & ( for x being Real holds f . x = min (d,(max (0,(b - |.((b * (x - a)) / c).|)))) ) holds
centroid (f,A) = centroid (f,['(a - c),(a + c)'])