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 Th48:
  <*[i,g]*> in [*i,g*]
proof
  [i,g] in FreeAtoms(H) by Th9;
  then <*[i,g]*> is FinSequence of FreeAtoms(H) by FINSEQ_1:74;
  then <*[i,g]*> in FreeAtoms(H)* by FINSEQ_1:def 11;
  then <*[i,g]*> in the carrier of FreeAtoms(H)*+^+<0> by MONOID_0:61;
  hence thesis by EQREL_1:20;
end;
