Theorems · Definition · general algebraic systems
Finsupp.piecewise
{α : Type u_1} →
{M : Type u_12} →
[inst : Zero M] → {P : α → Prop} → [DecidablePred P] → (Subtype P →₀ M) → ({ a // ¬P a } →₀ M) → α →₀ MCombine finitely supported functions over {a // P a} and {a // ¬P a}, by case-splitting on
P a.
- Defined in
- Mathlib.Data.Finsupp.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroDecidablePred
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.
- DFunLike.coeproof · cited by 62,936
- Finsuppstatement and proof · cited by 5,255
- Finsupp.supportproof · cited by 828
- Finset.mapproof · cited by 747
- Function.Embedding.subtypeproof · cited by 128
- Finset.disjUnionproof · cited by 55
Cited by5
Results whose statement or proof uses this declaration.
- Finsupp.extendDomainproof · cited by 11
- Finsupp.subtypeDomain_piecewisestatement · cited by 1
- Finsupp.subtypeDomain_not_piecewisestatement · cited by 0
- Finsupp.piecewise_applystatement and proof · cited by 0
- Finsupp.piecewise_supportstatement and proof · cited by 0