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;

theorem Th11:
  a,b,r are_collinear iff r in Line(a,b)
proof
  thus a,b,r are_collinear implies r in Line(a,b);
  thus r in Line(a,b) implies a,b,r are_collinear
  proof
    assume r in Line(a,b);
    then ex p st r=p & a,b,p are_collinear;
    hence thesis;
  end;
end;
