theorem Th80:
  for F being Function of [:D,D9:],E, f being Function of C,D,
      g being Function of C9,D9 holds (F*(f,g)).(c,c9) = F.(f.c,g.c9)
proof
  let F be Function of [:D,D9:],E, f be Function of C,D, g be Function of C9,
  D9;
  set H = F*(f,g);
  H is Function of [:C,C9:],E by Th78;
  then dom H = [:C,C9:] by FUNCT_2:def 1;
  then [c,c9] in dom H by ZFMISC_1:def 2;
  hence thesis by Th77;
end;
