theorem
  [.a,b,1_G.] = 1_G & [.a,1_G,b.] = 1_G & [.1_G,a,b.] = 1_G
proof
  thus [.a,b,1_G.] = 1_G by Th19;
  thus [.a,1_G,b.] = [.1_G,b.] by Th19
    .= 1_G by Th19;
  thus [.1_G,a,b.] = [.1_G,b.] by Th19
    .= 1_G by Th19;
end;
