reserve d,i,j,k,m,n,p,q,x,k1,k2 for Nat,
  a,c,i1,i2,i3,i5 for Integer;

theorem
  2 divides n iff n is even
proof
A1: n is even implies 2 divides n
  proof
    assume n is even;
    then n mod 2 = 0 by NAT_2:21;
    then ex k being Nat st n = 2*k + 0 & 0 < 2 by NAT_D:def 2;
    hence thesis;
  end;
  thus thesis by A1;
end;
