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;
reserve s,t for Element of FreeProduct(H);

theorem Th64:
  g <> 1_(H.i) implies nf [* i, g *] = <* [i,g] *>
proof
  assume g <> 1_(H.i);
  then A1: <* [i,g] *> is_a_normal_form_wrt ReductionRel H by Th38;
  [i,g] in FreeAtoms(H) by Th9;
  then <*[i,g]*> is FinSequence of FreeAtoms(H) by FINSEQ_1:74;
  hence thesis by A1, Th48, Def7;
end;
