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

theorem Th2:
  for G being Abelian right-distributive doubleLoop, a,b being
  Element of G holds a*(-b) = -(a*b)
proof
  let G be Abelian right-distributive doubleLoop, a,b be Element of G;
  a*b + a*(-b) = a*(b+ -b) by VECTSP_1:def 2
    .= a*0.G by Def1
    .= 0.G by ALGSTR_1:16;
  hence thesis by Def1;
end;
