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

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

• if the following are true:

  • a = b
  • b = c

  then a = c

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

• if sum of bit x bit 0 and bit 0 = x, then list (sum of bit x bit 0 and bit 0) and xs = list x and xs

• 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.