theorem Th53:
  Sgm P " X is without_zero finite Subset of NAT
proof
A1: Sgm P " X c= dom (Sgm P) by RELAT_1:132;
  dom (Sgm P) = Seg card P by FINSEQ_3:40;
  then not 0 in Sgm P"X by A1;
  hence thesis by A1,MEASURE6:def 2,XBOOLE_1:1;
end;
