reserve X for set, x,y,z for object,
  k,l,n for Nat,
  r for Real;

theorem Th1:
  for k being natural Number st r = k or r = -k holds r is Integer
proof
  let k be natural Number;
A1: k is Nat by TARSKI:1;
  assume r = k or r = -k;
  then r in INT by A1,Def1;
  hence thesis;
end;
