theorem Lm22b1: :: FUZZY_6:24

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