theorem Th33:
  L1 _|_ L2 implies ex x st L1 /\ L2 = {x}
  proof
    assume
A1: L1 _|_ L2;
    then
A2: L1 is being_line & L2 is being_line by EUCLIDLP:67;
A3: L1 <> L2 & L1 meets L2 by A1,EUCLIDLP:75,Th31,EUCLIDLP:109;
    not (ex x st L1 = {x} or L2 = {x}) by A2,Th7;
    hence thesis by A3,Th32;
  end;
