theorem Th37:
  (for d1,d2 holds h.(F.(d1,d2)) = H.(h.d1,h.d2)) implies
    h*(F.:(f,f9)) = H.:(h*f,h*f9)
proof
  assume
A1: for d1,d2 holds h.(F.(d1,d2)) = H.(h.d1,h.d2);
  now
    let c;
    thus (h*(F.:(f,f9))).c = h.((F.:(f,f9)).c) by FUNCT_2:15
      .= h.(F.(f.c,f9.c)) by FUNCOP_1:37
      .= H.(h.(f.c),h.(f9.c)) by A1
      .= H.((h*f).c,h.(f9.c)) by FUNCT_2:15
      .= H.((h*f).c,(h*f9).c) by FUNCT_2:15
      .= (H.:(h*f,h*f9)).c by FUNCOP_1:37;
  end;
  hence thesis by FUNCT_2:63;
end;
