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 Th58:
  I is trivial implies H.i, FreeProduct(H) are_isomorphic
proof
  assume I is trivial;
  then injection(H,i) is bijective by Th57;
  hence thesis by GROUP_6:def 11;
end;
