reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem
  n mod 2 = 0 or n mod 2 = 1
proof
  assume
A1: n mod 2 <> 0;
A2: 2 = 1 + 1;
  n mod 2 < 2 by Th1;
  then
A3: n mod 2 <= 1 by A2,NAT_1:13;
  n mod 2 >= 1 by A1,NAT_1:14;
  hence thesis by A3,XXREAL_0:1;
end;
