reserve i, j, k, l, m, n, t for Nat;

theorem
  n is even implies n div 2 = (n + 1) div 2
proof
  assume
A1: n is even;
  n = 2 * (n div 2) + (n mod 2) by NAT_D:2
    .= 2 * (n div 2) + 0 by A1,Th21;
  hence thesis by NAT_D:def 1;
end;
