Quiz (1 point)

• stack after popping a value from stack xs at index idx = reverse of (stack after popping a value from stack xs at index idx in traversed elements: [ ])
• stack after popping a value from stack [ x, xs ] at index idx in traversed elements: result = stack after popping a value from stack xs at index (idx - 1) in traversed elements: [ x, result ]
• 1 - 1 = 0
• stack after popping a value from stack [ x, xs ] at index 0 in traversed elements: result = result of dumping xs to result
• result of dumping [ y, [ ] ] to xs = [ y, xs ]
• reverse of [ x, [ y, [ ] ] ] = [ y, [ x, [ ] ] ]

• if 1 - 1 = 0, then stack after popping a value from stack [ 12, [ 14, [ ] ] ] at index (1 - 1) in traversed elements: [ 10, [ ] ] = stack after popping a value from stack [ 12, [ 14, [ ] ] ] at index 0 in traversed elements: [ 10, [ ] ]

• if the following are true:

  • a = b
  • b = c

  then a = c

• if the following are true:

  • a = b
  • b = c

  then a = c

• if the following are true:

  • a = b
  • b = c

  then a = c

• if stack after popping a value from stack [ 10, [ 12, [ 14, [ ] ] ] ] at index 1 in traversed elements: [ ] = [ 14, [ 10, [ ] ] ], then reverse of (stack after popping a value from stack [ 10, [ 12, [ 14, [ ] ] ] ] at index 1 in traversed elements: [ ]) = reverse of [ 14, [ 10, [ ] ] ]

• 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.