In this example, we prove that if we pop the following list

[3, [2, [1, []]]]

At index 2, the resulting list is

[3, [2, []]]

We use the "Begin Pop At Index Property" to set things up then rely on "Pop At Index Induction Example" to do most of the actual proof.

Quiz (1 point)

• remaining elements after xs is popped at index idx = remaining elements after xs is popped at index idx and visited stack is [ ]
• remaining elements after [ 3, [ 2, [ 1, [ ] ] ] ] is popped at index 2 and visited stack is [ ] = [ 3, [ 2, [ ] ] ]

• if the following are true:

  • a = b
  • b = c

  then a = c

Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.