theorem
  h |^ 2 = 1_G iff h" = h
proof
  thus h |^ 2 = 1_G implies h = h"
  proof
    assume h |^ 2 = 1_G;
    then h * h = 1_G by Th26;
    hence thesis by Th11;
  end;
  assume h = h";
  hence h |^ 2 = h * h" by Th26
    .= 1_G by Def5;
end;
