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
  a <> b implies ex P st a in P & b in P
proof
  assume a<>b;
  then reconsider P = Line(a,b) as LINE of CLSP by Def7;
  take P;
  thus thesis by Th10;
end;
