Theorems · Theorem · order theory
Set.rightInverse_rangeSplitting
∀ {α : Type u_1} {β : Type u_2} {f : α → β},
Function.Injective f → Function.RightInverse (Set.rangeFactorization f) (Set.rangeSplitting f)- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemstatement · cited by 7,166
- Set.rangestatement · cited by 4,705
- Set.rangeFactorizationstatement and proof · cited by 56
- Set.rangeSplittingstatement · cited by 23
- Set.leftInverse_rangeSplittingproof · cited by 3
- Function.LeftInverse.rightInverse_of_injectiveproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- MeasurableEmbedding.aemeasurable_comp_iffproof · cited by 2
- MeasurableEmbedding.measurable_comp_iffproof · cited by 2
- Set.preimage_rangeSplittingproof · cited by 1
- Set.leftInverse_rangeFactorization_iff_injectiveproof · cited by 0