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 Th28:
  for p,q being FinSequence of FreeAtoms(G)
  holds [p^<*[i,1_(G.i)]*>^q, p^q] in ReductionRel(G)
proof
  let p,q be FinSequence of FreeAtoms(G);
  [i,1_(G.i)] in FreeAtoms(G) by Th9;
  then reconsider s = <*[i,1_(G.i)]*> as FinSequence of FreeAtoms(G)
    by FINSEQ_1:74;
  p^s^q is FinSequence of FreeAtoms(G);
  hence thesis by Def3;
end;
