theorem Th66:
  M _|_ N implies ex p st p in M & p in N
proof
  reconsider M9=M,N9=N as Subset of the AffinStruct of POS;
  assume
A1: M _|_ N;
  then M is being_line;
  then
A2: M9 is being_line by Th43;
  N is being_line by A1,Th44;
  then
A3: N9 is being_line by Th43;
  not M // N by A1,Th52;
  then not M9 // N9 by Th46;
  hence thesis by A2,A3,AFF_1:58;
end;
