theorem Th24:
  F is associative implies F[;](d,id D)*(F.:(f,f9)) = F.:(F[;](d, id D)*f,f9)
proof
  assume
A1: F is associative;
  now
    let c;
    thus (F[;](d,id D)*(F.:(f,f9))).c = (F[;](d,id D)).((F.:(f,f9)).c) by
FUNCT_2:15
      .= (F[;](d,id D)).(F.(f.c,f9.c)) by FUNCOP_1:37
      .= F.(d,(id D).(F.(f.c,f9.c))) by FUNCOP_1:53
      .= F.(d,F.(f.c,f9.c))
      .= F.(F.(d,f.c),f9.c) by A1
      .= F.((F[;](d,f)).c,f9.c) by FUNCOP_1:53
      .= F.(((F[;](d,id D))*f).c,f9.c) by FUNCOP_1:55
      .= (F.:(F[;](d,id D)*f,f9)).c by FUNCOP_1:37;
  end;
  hence thesis by FUNCT_2:63;
end;
