reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem
  for a be non zero Nat holds
    ex k be odd Nat st a = 2|^(2 |-count a)*k
proof
  let a be non zero Nat;
  A1: 2 is non trivial; then
  consider k such that
  A2: a = (2|^(2 |-count a))*k by LmC1,NAT_D:def 3;
  not 2*2|^(2 |-count a) divides (2|^(2 |-count a))*k by A1,A2,LmC1; then
  k is odd by NEWTON02:2;
  hence thesis by A2;
end;
