Theorems · Theorem · order theory
Set.leftInverse_rangeSplitting
∀ {α : Type u_1} {β : Type u_2} (f : α → β), Function.LeftInverse (Set.rangeFactorization f) (Set.rangeSplitting f)- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.Elemstatement and proof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- Set.rangeFactorizationstatement · cited by 56
- Set.rangeSplittingstatement · cited by 23
- Set.apply_rangeSplittingproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- Set.rightInverse_rangeSplittingproof · cited by 4
- Set.rangeSplitting_injectiveproof · cited by 2
- Set.preimage_rangeSplittingproof · cited by 1