Function sum of a b and carry bit c

add stack a, stack b, and carry bit c and output the sum

Format:

sum of a b and carry bit c

Input:

list a -

list b -

bit c -

Output:

list - None

Properties that reference this function:

sum of (empty list) (empty list) and carry bit 0 = empty list (Add List Carry)

sum of (empty list) (empty list) and carry bit 1 = list 1 and (empty list) (Add List Carry (2))

sum of (list x and xs) (empty list) and carry bit 0 = list x and xs (Add List Carry (3))

sum of (list 0 and xs) (empty list) and carry bit 1 = list 1 and xs (Add List Carry (4))

sum of (list 1 and xs) (empty list) and carry bit 1 = list 0 and (sum of xs (empty list) and carry bit 1) (Add List Carry (5))

sum of (empty list) (list y and ys) and carry bit 0 = list y and ys (Add List Carry (6))

sum of (empty list) (list 0 and ys) and carry bit 1 = list 1 and ys (Add List Carry (7))

sum of (empty list) (list 1 and ys) and carry bit 1 = list 0 and (sum of (empty list) ys and carry bit 1) (Add List Carry (8))

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)) (Add List Carry (9))

sum of unsigned integers a and b = sum of a b and carry bit 0 (Add Unsigned Integer)

sum of x (empty list) and carry bit 0 = x (Add List Carry Property)

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