reserve s1,s2,q1 for Real_Sequence;
reserve n for Element of NAT;
reserve a,b for Real;

theorem Th14:
  for n be Nat holds ex k be Nat st n=2*k or n=2*k+1
proof
   let n be Nat;
   per cases;
   suppose n is even; then
    consider k be Nat such that
A1:  n = 2*k;
    take k;
    thus n=2*k or n=2*k+1 by A1;
   end;
   suppose n is odd; then
    n+1 is even; then
    consider k1 be Nat such that
A2:  n+1 = 2*k1;
    0 <> k1 by A2;
    then reconsider k=k1-1 as Nat;
    take k;
    thus n=2*k or n=2*k+1 by A2;
  end;
end;
