6. Like limit points, boundary points have an equivalent sequential definition. Lemma. Let SRn be a set. Let pRn. The point p is a boundary point of S if and only if there exists a sequence {x(k)}k in S and a sequence {y(k)}k in Sc both converging to p. You will study the proof of this lemma. Semeon bravely attempts to prove the "if" direction. 1. Let SRn. Let pRn. 2. Let {x(k)}k in S and {y(k)}k in Sc be sequences converging to p. 3. Fix >0. 4. There exists k1N+such that x(k1)p<. there exists k2n y this implies that b and are both non-empty. hence by definition p is a boundary point of s. while semeon proof has no serious flaws it missing important details. does not clearly state what he wants to prove. based on his writeup could appear after line use quantifiers write the formal statement show. three lines justifications. identify unjustified provide additional prove if direction lemma. include well-labeled illustration your proof. picture should be detailed enough so reader can look at grasp key ideas>