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 Th38:
  for X being set, b1, b2 being natural-valued ManySortedSet of X
  holds support (b1-'b2) c= support b1
proof
  let X be set, b1, b2 be natural-valued ManySortedSet of X;
  thus support (b1-'b2) c= support b1
  proof
    let x be object;
    assume
A1: x in support (b1-'b2);
    assume not x in support b1;
    then b1.x = 0 by Def7;
    then b1.x-'b2.x = 0 by NAT_2:8;
    then (b1-'b2).x = 0 by Def6;
    hence contradiction by A1,Def7;
  end;
end;
