
theorem Th6:
  for F be add-associative right_zeroed right_complementable
  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 distributive non
  empty doubleLoopStr, x,y be Element of F;
  thus (-x)*(-y) = -x*(-y) by Th5
    .= --x*y by Th4
    .= x*y by RLVECT_1:17;
end;
