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[Merged by Bors] - refactor(set_theory/game/nim): 0 ≈ nim 0 → nim 0 ≈ 0
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vihdzp
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| @[simp] theorem nim_one_equiv : star ≈ nim 1 := nim_one_relabelling.equiv | ||
| @[simp] theorem star_equiv_nim : star ≈ nim 1 := star_relabelling_nim.equiv | ||
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| @[simp] lemma nim_birthday (O : ordinal) : (nim O).birthday = O := |
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Note that if we flip the above we should ensure we have a simp lemma that says star.birthday = 1.
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We don't currently have said lemma, but I believe it would rather belong as a basic lemma on birthday.lean.
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0 ≈ nim 0 → nim 0 ≈ 00 ≈ nim 0 → nim 0 ≈ 0
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We invert the directions of a few simple equivalences/relabellings to a more natural order (simpler on the RHS).