reserve i, x, I for set,
  A, M for ManySortedSet of I,
  f for Function,
  F for ManySortedFunction of I;

theorem Th9:
  for M being non-empty ManySortedSet of I for X, Y being Element
  of M st X c= Y holds (id M)..X c= (id M)..Y
proof
  let M be non-empty ManySortedSet of I;
  let X, Y be Element of M such that
A1: X c= Y;
  (id M)..X = X by Th8;
  hence thesis by A1,Th8;
end;
