theorem :: CAT_4:43

for C being Cartesian_category
for a, b, c, d, e, s being Object of C
for f being Morphism of a,b
for h being Morphism of c,d
for g being Morphism of e,a
for k being Morphism of s,c st Hom (a,b) <> {} & Hom (c,d) <> {} & Hom (e,a) <> {} & Hom (s,c) <> {} holds
(f [x] h) * (g [x] k) = (f * g) [x] (h * k)