reserve x,y for set;

theorem
  for A, B being with_units non empty AltCatStr st A, B
  have_the_same_composition for a being Object of A, b being Object of B for o
being Object of Intersect(A, B) st o = a & o = b & idm a = idm b holds idm a in
  <^o,o^> by Th23;
