Quiz (1 point)

• result of sorting [ number, numbers ] with sorted stack sorted_list = result of sorting (remaining elements after [ number, numbers ] is popped at index (index of the mininum value in stack [ number, numbers ])) with sorted stack [ minimum value of stack [ number, numbers ], sorted_list ]
• minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 0, [ ] ]
• index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ]
• remaining elements after [ x, [ y, [ ] ] ] is popped at index [ 1, [ ] ] = [ x, [ ] ]
• result of sorting [ number, numbers ] with sorted stack sorted_list = result of sorting (remaining elements after [ number, numbers ] is popped at index (index of the mininum value in stack [ number, numbers ])) with sorted stack [ minimum value of stack [ number, numbers ], sorted_list ]
• index of the mininum value in stack [ x, [ ] ] = [ 0, [ ] ]
• remaining elements after [ [ x, [ ] ], [ ] ] is popped at index [ 0, [ ] ] = [ ]
• minimum value of stack [ x, [ ] ] = x
• result of sorting [ ] with sorted stack sort_list = sort_list
• result of sorting numbers = reverse of (result of sorting numbers with sorted stack [ ])
• reverse of [ [ x, [ ] ], [ [ y, [ ] ], [ ] ] ] = [ [ y, [ ] ], [ [ x, [ ] ], [ ] ] ]

• if minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 0, [ ] ], then [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = [ [ 0, [ ] ], [ ] ]

• if index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ 1, [ ] ], then remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) = remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index [ 1, [ ] ]

• if the following are true:

  • a = b
  • b = c

  then a = c

• if remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]) = [ [ 1, [ ] ], [ ] ], then result of sorting (remaining elements after [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ]

• if [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = [ [ 0, [ ] ], [ ] ], then result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], [ ] ] = result of sorting [ [ 1, [ ] ], [ ] ] with sorted stack [ [ 0, [ ] ], [ ] ]

• if the following are true:

  • a = b
  • b = c

  then a = c

• if index of the mininum value in stack [ [ 1, [ ] ], [ ] ] = [ 0, [ ] ], then remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ]) = remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index [ 0, [ ] ]

• if the following are true:

  • a = b
  • b = c

  then a = c

• if remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ]) = [ ], then result of sorting (remaining elements after [ [ 1, [ ] ], [ ] ] is popped at index (index of the mininum value in stack [ [ 1, [ ] ], [ ] ])) with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ]

• if minimum value of stack [ [ 1, [ ] ], [ ] ] = [ 1, [ ] ], then [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]

• if [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], then result of sorting [ ] with sorted stack [ minimum value of stack [ [ 1, [ ] ], [ ] ], [ [ 0, [ ] ], [ ] ] ] = result of sorting [ ] with sorted stack [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]

• 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 the following are true:

  • a = b
  • b = c

  then a = c

• if the following are true:

  • a = b
  • b = c

  then a = c

• if result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ] = [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ], then reverse of (result of sorting [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ] with sorted stack [ ]) = reverse of [ [ 1, [ ] ], [ [ 0, [ ] ], [ ] ] ]

• 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.