
theorem
  for T being Nat holds
    {w where w is Element of NAT: w <= T} is non empty Subset of NAT
proof
  let T be Nat;
  B1: {w where w is Element of NAT: w <= T} c= NAT
  proof
    let x be object;
    assume x in {w where w is Element of NAT: w <= T};
    then consider w being Element of NAT such that C1: x=w & w<=T;
   thus thesis by C1;
  end;
   T in {w where w is Element of NAT: w <= T}
   proof
    T in NAT by ORDINAL1:def 12;
    hence thesis;
   end;
  hence thesis by B1;
end;
