Quiz (1 point)

• 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))
• sum of bit 0 bit 0 and bit 0 = 0
• carry on sum of bit 0 bit 0 and 0 = 0
• sum of (empty list) (empty list) and carry bit 0 = empty list

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

• if the following are true:

  • a = b
  • b = c

  then a = c

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

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

• if the following are true:

  • a = b
  • b = c

  then a = c

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

• 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.