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

theorem Lem7:
  for a,b,c being bag of I st a divides b divides c holds a divides c
  proof
    let a,b,c be bag of I; assume that
A1: for x being object holds a.x <= b.x and
A2: for x being object holds b.x <= c.x;
    let x be object;
    a.x <= b.x <= c.x by A1,A2;
    hence thesis by XXREAL_0:2;
  end;
