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- Lemma 1: When all soldiers meet => P position.
- Lemma 2: Strategy of a game of modified nim can be obtained from a game of normal nim. One of the generals can ensure a win. This is because the game of warlords can be modelled after a game of nim. Since we know that the game of nim has a terminal position, the game of warlords will also terminate.
- Ultimate proof:
- A position in warlords is a P position iff the corresponding normal nim is a P position.
- Case 1: AFSOC a P position in warlords is a N position in nim.
- Case 2: AFSOC a N position in warlords is a P position in nim.
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