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This proof proves the theorem
 a:{...0}. n:{...-1}. a rem n = -(-a rem -n)
The following lemmas are used in this proof:
- div_3_to_1
- a:{...0}. b:{...-1}. a
 b = -a -b
- rem_to_div
- a:
 . n:  . a rem n = a - (a n) * n
Please do the following and record your answers:
- Translate this proof into English.
- Was there any part of this proof that you found difficult to translate? If
so, why?
- Do you think that this theorem was proved in a natural or intuitive
manner or not? If so, why?
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