lean-ja / lean-ja/lean-by-example
謎: 選択公理なしで単射の像からの逆写像の存在がいえるか？
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付録アイデア
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- Lean
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- 188
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Description
ZFにおいて、「f : X → Yが単射であるとき、f の像からの逆写像 g : Im f → Xがある」は選択公理なしで示せる。
しかし、Leanでこれを Classical.choice なしで示す方法がわからない。
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
The issue mentions no file, test, or entry point. First locate the Lean example or theorem corresponding to an injective function and its image, then investigate how to express the inverse without Classical.choice; done means a checked Lean proof in the relevant example.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 25/100