theorem
  g. [.a1,a2,a3.] = [.g.a1,g.a2,g.a3.]
proof
  thus g. [.a1,a2,a3.] = g. [.[.a1,a2.],a3.] by GROUP_5:def 3
    .= [.g. [.a1,a2.],g.a3.] by Th34
    .= [.[.g.a1,g.a2.],g.a3.] by Th34
    .= [.g.a1,g.a2,g.a3.] by GROUP_5:def 3;
end;
