Theorems · Theorem · order theory
Set.preimage_rangeSplitting
∀ {α : Type u_1} {β : Type u_2} {f : α → β},
Function.Injective f → Set.preimage (Set.rangeSplitting f) = Set.image (Set.rangeFactorization f)- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Set.imagestatement · cited by 5,609
- Set.preimagestatement · cited by 4,946
- Set.rangestatement · cited by 4,705
- Set.rangeFactorizationstatement · cited by 56
- Set.image_eq_preimage_of_inverseproof · cited by 27
- Set.rangeSplittingstatement · cited by 23
- Set.rightInverse_rangeSplittingproof · cited by 4
- Set.leftInverse_rangeSplittingproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MeasurableEmbedding.measurable_rangeSplittingproof · cited by 3