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 Th16:
  p in P & q in P & r in P implies p,q,r are_collinear
proof
  assume that
A1: p in P & q in P and
A2: r in P;
  consider a,b such that
A3: a<>b and
A4: P = Line(a,b) by Def7;
A5: ex z be Point of CLSP st z=r & a,b,z are_collinear by A2,A4;
  ( ex x be Point of CLSP st x=p & a,b,x are_collinear)& ex y be Point of
  CLSP st y=q & a,b,y are_collinear by A1,A4;
  hence thesis by A3,A5,Th3;
end;
