theorem Lm22b1p: :: FUZZY_7:41

for a, b, c being Real
for f, g being Function of REAL,REAL
for h being PartFunc 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 & [.a,c.] c= dom h holds
h | [.a,c.] is continuous