theorem Th49:
  X has_upper_Zorn_property_wrt R implies X <> {}
proof
  assume
A1: for Y st Y c= X & R|_2 Y is being_linear-order ex x st x in X & for
  y st y in Y holds [y,x] in R;
  R|_2 {} is being_linear-order by Lm17;
  then ex x st x in X & for y st y in {} holds [y,x] in R by A1,XBOOLE_1:2;
  hence thesis;
end;
