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 Th49:
  for n being set, b,b1,b2 being bag of n st b = b1 + b2 holds b1 divides b
proof
  let n be set, b,b1,b2 be bag of n;
  assume
A1: b = b1 + b2;
  now
    let k be object;
    assume k in n;
    b.k = b1.k+b2.k by A1,Def5;
    hence b1.k <= b.k by NAT_1:11;
  end;
  hence thesis by Th45;
end;
