theorem
  [* i, g *]" = [* i, g" *]
proof
  [* i,g *] * [* i,g" *] = [* i,g*g" *] by Th51
    .= [* i,1_(H.i) *] by GROUP_1:def 5
    .= 1_FreeProduct(H) by Th49;
  hence thesis by GROUP_1:12;
end;
