In step 2, we state that the reverse of

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

is

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

Then we prepend 4 to this list in step 3, which leads to:

[4,[3,[2,[1,[]]]]]

Then step 5 shows that the reverse of the above list is:

[1,[2,[3,[4,[]]]]]

Quiz (1 point)

• result of appending y to xs = reverse of [ y, reverse of xs ]
• reverse of [ 1, [ 2, [ 3, [ ] ] ] ] = [ 3, [ 2, [ 1, [ ] ] ] ]
• reverse of [ 4, [ 3, [ 2, [ 1, [ ] ] ] ] ] = [ 1, [ 2, [ 3, [ 4, [ ] ] ] ] ]

• if reverse of [ 1, [ 2, [ 3, [ ] ] ] ] = [ 3, [ 2, [ 1, [ ] ] ] ], then [ 4, reverse of [ 1, [ 2, [ 3, [ ] ] ] ] ] = [ 4, [ 3, [ 2, [ 1, [ ] ] ] ] ]

• if [ 4, reverse of [ 1, [ 2, [ 3, [ ] ] ] ] ] = [ 4, [ 3, [ 2, [ 1, [ ] ] ] ] ], then reverse of [ 4, reverse of [ 1, [ 2, [ 3, [ ] ] ] ] ] = reverse of [ 4, [ 3, [ 2, [ 1, [ ] ] ] ] ]

• if the following are true:

  • a = b
  • b = c

  then a = c

• 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.