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fix: part-label Example 3.5.10 Verso docstrings #638

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fix: part-label Example 3.5.10 Verso docstrings #638

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10 changes: 5 additions & 5 deletions Analysis/Section_3_5.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -199,7 +199,7 @@ noncomputable abbrev SetTheory.Set.prod_associator (X Y Z:Set) : (X ×ˢ Y) ×ˢ
right_inv _ := by simp

/--
Example 3.5.10. I suspect most of the equivalences will require classical reasoning and only be
Example 3.5.10 (a). I suspect most of the equivalences will require classical reasoning and only be
defined non-computably, but would be happy to learn of counterexamples.
-/
noncomputable abbrev SetTheory.Set.singleton_iProd_equiv (i:Object) (X:Set) :
Expand All @@ -209,30 +209,30 @@ noncomputable abbrev SetTheory.Set.singleton_iProd_equiv (i:Object) (X:Set) :
left_inv := sorry
right_inv := sorry

/-- Example 3.5.10 -/
/-- Example 3.5.10 (b) -/
abbrev SetTheory.Set.empty_iProd_equiv (X: (∅:Set) → Set) : iProd X ≃ Unit where
toFun := sorry
invFun := sorry
left_inv := sorry
right_inv := sorry

/-- Example 3.5.10 -/
/-- Example 3.5.10 (c) -/
noncomputable abbrev SetTheory.Set.iProd_of_const_equiv (I:Set) (X: Set) :
iProd (fun _:I ↦ X) ≃ (I → X) where
toFun := sorry
invFun := sorry
left_inv := sorry
right_inv := sorry

/-- Example 3.5.10 -/
/-- Example 3.5.10 (d) -/
noncomputable abbrev SetTheory.Set.iProd_equiv_prod (X: ({0,1}:Set) → Set) :
iProd X ≃ (X ⟨ 0, by simp ⟩) ×ˢ (X ⟨ 1, by simp ⟩) where
toFun := sorry
invFun := sorry
left_inv := sorry
right_inv := sorry

/-- Example 3.5.10 -/
/-- Example 3.5.10 (e) -/
noncomputable abbrev SetTheory.Set.iProd_equiv_prod_triple (X: ({0,1,2}:Set) → Set) :
iProd X ≃ (X ⟨ 0, by simp ⟩) ×ˢ (X ⟨ 1, by simp ⟩) ×ˢ (X ⟨ 2, by simp ⟩) where
toFun := sorry
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