Theorems · Definition · logic and foundations
Set.rangeSplitting
{α : Type u} → {β : Type v} → (f : α → β) → ↑(Set.range f) → αWe can use the axiom of choice to pick a preimage for every element of range f.
- Defined in
- Mathlib.Data.Set.Operations
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by24
Results whose statement or proof uses this declaration.
- LinearIndependent.linearIndepOn_idproof · cited by 14
- Set.apply_rangeSplittingstatement · cited by 8
- lift_rank_range_leproof · cited by 7
- Set.rightInverse_rangeSplittingstatement · cited by 4
- Set.comp_rangeSplittingstatement · cited by 4
- Equiv.Set.rangeSplittingImageEquivstatement and proof · cited by 3
- Filter.EventuallyConst.of_monotone_of_lt_cofproof · cited by 3
- MeasurableEmbedding.measurable_rangeSplittingstatement · cited by 3
- Set.leftInverse_rangeSplittingstatement · cited by 3
- MeasurableEmbedding.measurable_comp_iffproof · cited by 2
- MeasurableEmbedding.aemeasurable_comp_iffproof · cited by 2
- Set.rangeSplitting_injectivestatement · cited by 2