reserve X for set;
reserve CS for non empty CollStr;
reserve a,b,c for Point of CS;
reserve CLSP for CollSp;
reserve a,b,c,d,p,q,r for Point of CLSP;
reserve i,j,k for Element of NAT;
reserve CLSP for proper CollSp;
reserve a,b,c,p,q,r for Point of CLSP;
reserve P,Q for LINE of CLSP;

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;
