Quiz (1 point)

• index of value value in numbers = index of value value in numbers with current index [ 0, [ ] ]
• not (1 = 0)
• sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ] = [ 1, [ ] ]
• [0,[]] = [0,[]]
• if not(x = y), then [x,xs] ≠ [y,ys]
• if are_not_equal_list(number, value): find_number_index([number, remain], value, index) == find_number_index(remain, value, add_uint(index, [1, []]))

• if sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ] = [ 1, [ ] ], then index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index (sum of unsigned integers [ 0, [ ] ] and [ 1, [ ] ]) = index of value [ 0, [ ] ] in [ [ 0, [ ] ], [ ] ] with current index [ 1, [ ] ]

• if the following are true:

  • a = b
  • b = c

  then a = c

• if are_equal_list(number, value): find_number_index([number, remain], value, index) == index

• 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.