reserve a,b for object, I,J for set;

theorem
  for M being RelExtension of finite-MultiSet_over I holds
  the carrier of M = Bags I
  proof set N = finite-MultiSet_over I;
    let M be RelExtension of finite-MultiSet_over I;
    thus the carrier of M c= Bags I
    proof let a;
      assume a in the carrier of M;
      hence a in Bags I by PRE_POLY:def 12;
    end;
    let a; assume a in Bags I;
    then a is bag of I by PRE_POLY:def 12;
    then a is Element of N by Th1;
    then a is Element of M by Th2;
    hence thesis;
  end;
