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 Th29:
  [<*[i,1_(G.i)]*>,{}] in ReductionRel(G)
proof
  set p = <*>FreeAtoms(G);
  [p^<*[i,1_(G.i)]*>^p, p^p] = [<*[i,1_(G.i)]*>^p, p^p] by FINSEQ_1:34
    .= [<*[i,1_(G.i)]*>, p^p] by FINSEQ_1:34
    .= [<*[i,1_(G.i)]*>, {}];
  hence thesis by Th28;
end;
