
theorem Th28:
  for L be add-associative right_zeroed right_complementable
right-distributive non empty doubleLoopStr for v be Element of L holds v*0_.(
  L) = 0_.(L)
proof
  let L be add-associative right_zeroed right_complementable
  right-distributive non empty doubleLoopStr;
  let v be Element of L;
  now
    let n be Element of NAT;
    thus (0_.(L)).n = 0.L by FUNCOP_1:7
      .= v*0.L
      .= v*(0_.(L)).n by FUNCOP_1:7;
  end;
  hence thesis by Def4;
end;
