theorem Th34:
  g. [.a,b.] = [.g.a,g.b.]
proof
  thus g. [.a,b.] = g.(a" * b" * a * b) by GROUP_5:16
    .= g.(a" * b" * a) * g.b by Def6
    .= g.(a" * b") * g.a * g.b by Def6
    .= g.(a") * g.(b") * g.a * g.b by Def6
    .= (g.a)" * g.(b") * g.a * g.b by Th32
    .= (g.a)" * (g.b)" * g.a * g.b by Th32
    .= [.g.a,g.b.] by GROUP_5:16;
end;
