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

theorem Th26:
  for p being Bags I-valued FinSequence st b in rng p holds b divides Sum p
  proof
    let p be Bags I-valued FinSequence;
    assume b in rng p;
    then consider q,r being FinSequence such that
A1: p = q^<*b*>^r by Lem9;
    reconsider qb = q^<*b*>, r as Bags I-valued FinSequence by A1,Lem8;
    qb = qb;
    then reconsider q as Bags I-valued FinSequence by Lem8;
    Sum p = Sum(q^<*b*>)+Sum r = Sum q + b + Sum r = Sum r+Sum q+b
    by A1,Th22,Th24,RFUNCT_1:8;
    hence b divides Sum p by PRE_POLY:50;
  end;
