theorem
  K is being_line implies ex x st a,x _|_ K & x in K
proof
  assume K is being_line;
  then consider p,q such that
A1: p<>q and
A2: K = Line(p,q);
  consider x such that
A3: a,x _|_ p,q and
A4: LIN p,q,x by Th69;
  take x;
  thus a,x _|_ K by A1,A2,A3;
  thus thesis by A2,A4,Def10;
end;
