reserve o,m for set;
reserve C for Cartesian_category;
reserve a,b,c,d,e,s for Object of C;

theorem
  for f being Morphism of c,a, g being Morphism of c,b st Hom(c,a) <> {}
  & Hom(c,b) <> {} holds <:f,g:> = (f[x]g)*Delta(c)
proof
  let f be Morphism of c,a, g be Morphism of c,b such that
A1: Hom(c,a) <> {} and
A2: Hom(c,b) <> {};
  Hom(c,c) <> {};
  hence (f[x]g)*Delta(c) = <:f*(id c),g*(id c):> by A1,A2,Th41
    .= <:f,g*(id c):> by A1,CAT_1:29
    .= <:f,g:> by A2,CAT_1:29;
end;
