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
  for P ex a,b st a<>b & a in P & b in P
proof
  let P;
  consider a,b such that
A1: a<>b & P = Line(a,b) by Def7;
  take a,b;
  thus thesis by A1,Th10;
end;
