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This proof proves the theorem
 a: . b:  . a rem -b = a rem b
The following lemmas are used in this proof:
- rem_2_to_1
- a:{...0}. n:
  . a rem n = -(-a rem n)
- rem_3_to_1
- a:{...0}. n:{...-1}. a rem n = -(-a rem -n)
- rem_4_to_1
- a:. n:{...-1}. a rem n = a rem -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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