reserve L for non empty doubleLoopStr;
reserve a,b,c,x,y,z for Element of L;

theorem
  for G being Abelian right-distributive doubleLoop holds (-1.G)*(-1.G) = 1.G
proof
  let G be Abelian right-distributive doubleLoop;
  thus (-1.G)*(-1.G) = -((-1.G)*1_G) by Th2
    .= -(-1.G)
    .= 1.G by Th3;
end;
