reserve A for set, x,y,z for object,
  k for Element of NAT;
reserve n for Nat,
  x for object;
reserve V, C for set;

theorem
  for X being set, b, c, d being natural-valued ManySortedSet of X holds
  b-'c-'d = b-'(c+d)
proof
  let X be set, b, c, d be natural-valued ManySortedSet of X;
  now
    let x be object;
    assume x in X;
    thus (b-'c-'d).x = (b-'c).x -' d.x by Def6
      .= b.x-'c.x-'d.x by Def6
      .= b.x-'(c.x+d.x) by NAT_2:30
      .= b.x-'(c+d).x by Def5;
  end;
  hence thesis by Th33;
end;
