Theorems · Definition · general algebraic systems
DFinsupp.equivProdDFinsupp
{ι : Type u} →
{α : Option ι → Type v} →
[inst : (i : Option ι) → Zero (α i)] → (Π₀ (i : Option ι), α i) ≃ α none × Π₀ (i : ι), α (some i)Bijection obtained by separating the term of index none of a dfinsupp over Option ι.
This is the dfinsupp version of Equiv.piOptionEquivProd.
- Defined in
- Mathlib.Data.DFinsupp.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Zero
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
- Equivstatement · cited by 8,337
- DFinsuppstatement and proof · cited by 694
- Option.some_injectiveproof · cited by 31
- DFinsupp.comapDomainproof · cited by 8
- DFinsupp.extendWithproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- DirectSum.addEquivProdDirectSumproof · cited by 5
- DFinsupp.equivProdDFinsupp_addstatement · cited by 0
- DFinsupp.equivProdDFinsupp_applystatement and proof · cited by 0
- DFinsupp.equivProdDFinsupp_smulstatement · cited by 0
- DFinsupp.equivProdDFinsupp_symm_applystatement and proof · cited by 0