Quiz (1 point)

• (list x and xs) multiplied by (list y and (list y2 and ys)) = sum of unsigned integers (list x and xs) and ((list x and xs) multiplied by (decrement (list y and (list y2 and ys)) by 1))
• decrement (list 0 and (list 1 and (empty list))) by 1 = list 1 and (empty list)
• (list x and xs) multiplied by (list 1 and (empty list)) = list x and xs
• sum of unsigned integers (list 1 and (list 1 and (empty list))) and (list 1 and (list 1 and (empty list))) = list 0 and (list 1 and (list 1 and (empty list)))

• if decrement (list 0 and (list 1 and (empty list))) by 1 = list 1 and (empty list), then (list 1 and (list 1 and (empty list))) multiplied by (decrement (list 0 and (list 1 and (empty list))) by 1) = (list 1 and (list 1 and (empty list))) multiplied by (list 1 and (empty list))

• if the following are true:

  • a = b
  • b = c

  then a = c

• if (list 1 and (list 1 and (empty list))) multiplied by (decrement (list 0 and (list 1 and (empty list))) by 1) = list 1 and (list 1 and (empty list)), then sum of unsigned integers (list 1 and (list 1 and (empty list))) and ((list 1 and (list 1 and (empty list))) multiplied by (decrement (list 0 and (list 1 and (empty list))) by 1)) = sum of unsigned integers (list 1 and (list 1 and (empty list))) and (list 1 and (list 1 and (empty list)))

• 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.