Properties

sum of unsigned integers a and b = sum of a b and carry bit 0

decrement (list 0 and (list 1 and (empty list))) by 1 = list 1 and (empty list)

decrement (list 0 and (list 1 and (list x and xs))) by 1 = list 1 and (list 0 and (list x and xs))

decrement (list 1 and xs) by 1 = list 0 and xs

(list x and xs) multiplied by (list 0 and (empty list)) = list 0 and (empty list)

(list 0 and (empty list)) multiplied by (list y and ys) = list 0 and (empty list)

(list x and xs) multiplied by (list 1 and (empty list)) = list x and xs

(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))

sum of bit x bit 0 and bit 0 = x

carry on sum of bit x bit 0 and 0 = 0

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

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