Theorems · Definition · combinatorics
Finset.piecewise
{ι : Type u_1} →
{π : ι → Sort u_2} →
(s : Finset ι) → ((i : ι) → π i) → ((i : ι) → π i) → [(j : ι) → Decidable (j ∈ s)] → (i : ι) → π is.piecewise f g is the function equal to f on the finset s, and to g on its
complement.
- Defined in
- Mathlib.Data.Finset.Piecewise
- Cited by
- 64 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Decidable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
Cited by65
Results whose statement or proof uses this declaration.
- Finset.piecewise_eq_of_memstatement · cited by 13
- Finset.piecewise_eq_of_notMemstatement · cited by 12
- BoxIntegral.TaggedPrepartition.disjUnionproof · cited by 10
- Finset.piecewise_emptystatement · cited by 7
- Finset.piecewise_insertstatement · cited by 6
- Finset.sum_inter_add_sum_sdiffproof · cited by 5
- Finset.piecewise_congrstatement · cited by 4
- MultilinearMap.map_add_univstatement and proof · cited by 4
- MultilinearMap.map_piecewise_smulstatement and proof · cited by 4
- isPreconnected_univ_piproof · cited by 4
- FormalMultilinearSeries.changeOriginSeriesTerm_applystatement · cited by 3
- Finset.piecewise_singletonstatement and proof · cited by 3