theorem Th82:
  (F*(id D,u)).:(f,f9) = F.:(f,u*f9)
proof
  now
    let c;
    thus ((F*(id D,u)).:(f,f9)).c = (F*(id D,u)).(f.c,f9.c) by FUNCOP_1:37
      .= F.(f.c,u.(f9.c)) by Th81
      .= F.(f.c,(u*f9).c) by FUNCT_2:15
      .= (F.:(f,u*f9)).c by FUNCOP_1:37;
  end;
  hence thesis by FUNCT_2:63;
end;
