reserve F for Field,
  x for Element of F,
  V for VectSp of F,
  v for Element of V;

theorem
  for L be add-associative right_zeroed right_complementable
right-distributive unital non empty doubleLoopStr for n be Element of NAT st
  n > 0 holds (power L).(0.L,n) = 0.L
proof
  let L be add-associative right_zeroed right_complementable
  right-distributive unital non empty doubleLoopStr;
  let n be Element of NAT;
  assume n > 0;
  then
A1: n >= 0+1 by NAT_1:13;
  n = n-1+1 .= n-'1+1 by A1,XREAL_0:def 2,XREAL_1:19;
  hence (power L).(0.L,n) = (power L).(0.L,n-'1)*0.L by GROUP_1:def 7
    .= 0.L;
end;
