Theorems · Theorem · order theory
Set.domRestrict_piecewise_compl
∀ {α : Type u_1} {β : Type u_2} (f g : α → β) (s : Set α) [inst : (x : α) → Decidable (x ∈ s)],
sᶜ.domRestrict (s.piecewise f g) = sᶜ.domRestrict g- Defined in
- Mathlib.Data.Set.Restrict
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses Quot.sound
- Assumes
- Decidable
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.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement · cited by 7,166
- Compl.complstatement · cited by 2,925
- Set.domRestrictstatement · cited by 383
- Set.piecewisestatement · cited by 136
- Set.domRestrict_ite_complproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- AEMeasurable.sum_measureproof · cited by 3
- MeasureTheory.NullMeasurable.aemeasurableproof · cited by 1
- Set.restrict_piecewise_complproof · cited by 0