Theorems · Theorem · logic and foundations
Set.apply_rangeSplitting
∀ {α : Type u} {β : Type v} (f : α → β) (x : ↑(Set.range f)), f (Set.rangeSplitting f x) = ↑x- Defined in
- Mathlib.Data.Set.Operations
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 7,166
- Set.rangestatement and proof · cited by 4,705
- Set.rangeSplittingstatement · cited by 23
Cited by8
Results whose statement or proof uses this declaration.
- Set.comp_rangeSplittingproof · cited by 4
- Set.leftInverse_rangeSplittingproof · cited by 3
- Filter.EventuallyConst.of_not_isCofinal_rangeSplittingproof · cited by 1
- Set.Definable.image_compproof · cited by 1
- Set.rangeSplitting_strictMonoproof · cited by 1
- MeasureTheory.tendsto_diracProbaEquivSymm_iff_tendstoproof · cited by 1
- Metric.secondCountable_of_countable_discretizationproof · cited by 0
- Equiv.coe_ofInjective_symmproof · cited by 0