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 Th26:
  for p,q being FinSequence of FreeAtoms(G), g,h being Element of G.i
  holds [p^<*[i,g],[i,h]*>^q, p^<*[i,g*h]*>^q] in ReductionRel(G)
proof
  let p,q be FinSequence of FreeAtoms(G), g,h being Element of G.i;
  [i,g] in FreeAtoms(G) & [i,h] in FreeAtoms(G) & [i,g*h] in FreeAtoms(G)
    by Th9;
  then reconsider s = <*[i,g],[i,h]*>, t = <*[i,g*h]*>
    as FinSequence of FreeAtoms(G) by FINSEQ_1:74, FINSEQ_2:13;
  p^s^q is FinSequence of FreeAtoms(G) &
    p^t^q is FinSequence of FreeAtoms(G);
  hence thesis by Def3;
end;
