theorem Th19:
  p<>q & p in P & q in P implies Line(p,q) = P
proof
  assume that
A1: p<>q and
A2: p in P & q in P;
  reconsider Q = Line(p,q) as LINE of CLSP by A1,Def7;
  Q c= P by A1,A2,Th18;
  hence thesis by Th17;
end;
