theorem :: FUZZY_6:21

for a, b, c being Real
for f, g, h being Function of REAL,REAL st a <= b & b <= c & f | ['a,c'] is bounded & g | ['a,c'] is bounded & h = (f | [.a,b.]) +* (g | [.b,c.]) & f . b = g . b holds
h | ['a,c'] is bounded