reserve x,y,z for object, X for set, I for non empty set, i,j for Element of I,
    M0 for multMagma-yielding Function,
    M for non empty multMagma-yielding Function,
    M1, M2, M3 for non empty multMagma,
    G for Group-like multMagma-Family of I,
    H for Group-like associative multMagma-Family of I;
reserve p, q for FinSequence of FreeAtoms(H), g,h for Element of H.i,
  k for Nat;

theorem
  for g being Element of G.i, h being Element of G.j
  holds <*[i,g],[j,h]*> is FinSequence of FreeAtoms(G)
proof
  let g be Element of G.i, h be Element of G.j;
  [i,g] in FreeAtoms(G) & [j,h] in FreeAtoms(G) by Th9;
  hence thesis by FINSEQ_2:13;
end;
