Quiz (1 point)

• sum of unsigned integers a and b = sum of a b and carry bit 0
• sum of (list x and xs) (list y and ys) and carry bit carry = list (sum of bit x bit y and bit carry) and (sum of xs ys and carry bit (carry on sum of bit x bit y and carry))
• carry on sum of bit 1 bit 1 and 0 = 1
• sum of (list x and xs) (list y and ys) and carry bit carry = list (sum of bit x bit y and bit carry) and (sum of xs ys and carry bit (carry on sum of bit x bit y and carry))
• carry on sum of bit 1 bit 1 and 1 = 1
• sum of (empty list) (empty list) and carry bit 1 = list 1 and (empty list)
• sum of bit 1 bit 1 and bit 1 = 1
• sum of bit 1 bit 1 and bit 0 = 0

• if carry on sum of bit 1 bit 1 and 0 = 1, then sum of (list 1 and (empty list)) (list 1 and (empty list)) and carry bit (carry on sum of bit 1 bit 1 and 0) = sum of (list 1 and (empty list)) (list 1 and (empty list)) and carry bit 1

• if carry on sum of bit 1 bit 1 and 1 = 1, then sum of (empty list) (empty list) and carry bit (carry on sum of bit 1 bit 1 and 1) = sum of (empty list) (empty list) and carry bit 1

• if the following are true:

  • a = b
  • b = c

  then a = c

• if sum of (empty list) (empty list) and carry bit (carry on sum of bit 1 bit 1 and 1) = list 1 and (empty list), then list (sum of bit 1 bit 1 and bit 1) and (sum of (empty list) (empty list) and carry bit (carry on sum of bit 1 bit 1 and 1)) = list (sum of bit 1 bit 1 and bit 1) and (list 1 and (empty list))

• if sum of bit 1 bit 1 and bit 1 = 1, then list (sum of bit 1 bit 1 and bit 1) and (list 1 and (empty list)) = 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

• if the following are true:

  • a = b
  • b = c

  then a = c

• if sum of (list 1 and (empty list)) (list 1 and (empty list)) and carry bit (carry on sum of bit 1 bit 1 and 0) = list 1 and (list 1 and (empty list)), then list (sum of bit 1 bit 1 and bit 0) and (sum of (list 1 and (empty list)) (list 1 and (empty list)) and carry bit (carry on sum of bit 1 bit 1 and 0)) = list (sum of bit 1 bit 1 and bit 0) and (list 1 and (list 1 and (empty list)))

• if sum of bit 1 bit 1 and bit 0 = 0, then list (sum of bit 1 bit 1 and bit 0) and (list 1 and (list 1 and (empty list))) = list 0 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

• 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.