
theorem Th10:
  for I being non empty set, J being TopStruct-yielding non-Empty
  ManySortedSet of I, i being Element of I holds
  proj(J,i)"[#](J.i) = [#] product J
proof
  let I be non empty set, J be TopStruct-yielding non-Empty ManySortedSet of I,
  i be Element of I;
  i in I;
  then i in dom Carrier J by PARTFUN1:def 2;
  then proj(Carrier J,i)"((Carrier J).i) = product Carrier J by Th4;
  then proj(Carrier J,i)"((Carrier J).i) = [#] product J by WAYBEL18:def 3;
  then proj(Carrier J,i)"[#](J.i) = [#] product J by YELLOW_6:2;
  hence thesis by WAYBEL18:def 4;
end;
