theorem Th43:
  for N be finite without_zero Subset of NAT holds N is included_in_Seg
proof
  let N be finite without_zero Subset of NAT;
  consider k be Nat such that
A1: for n be Nat st n in N holds n<=k by STIRL2_1:56;
  take k;
  N c= Seg k
  proof
    let x be object;
    assume
A2: x in N;
    then consider n be Element of NAT such that
A3: n=x;
A4: n>=1 by A2,A3,NAT_1:14;
    n<=k by A1,A2,A3;
    hence thesis by A3,A4;
  end;
  hence thesis;
end;
