
theorem
  for i being Integer st i is Element of NAT holds i div 2 is Element of NAT
proof
  let i be Integer;
  assume i is Element of NAT;
  then reconsider n = i as Element of NAT;
  i/2 - 1 < [\i/2/] by INT_1:def 6;
  then
A1: i/2 < [\i/2/]+1 by XREAL_1:19;
  n >= 0;
  then i/2 >= 0/2;
  then [\i/2/] is Element of NAT by A1,INT_1:3,7;
  hence thesis by INT_1:def 9;
end;
