
theorem Th5:
  for F be add-associative right_zeroed right_complementable
  left-distributive non empty doubleLoopStr, x,y being Element of F holds
  (-x)*y = -x*y
proof
  let F be add-associative right_zeroed right_complementable left-distributive
  non empty doubleLoopStr, x,y be Element of F;
  x*y +(-x)*y = (x+(-x))*y by Def3
    .= (0.F)*y by RLVECT_1:def 10
    .= 0.F;
  hence thesis by RLVECT_1:def 10;
end;
