Theorems · Theorem · group theory
DirectSum.coeAddMonoidHom_eq_dfinsuppSum
∀ {ι : Type v} [inst : DecidableEq ι] {M : Type u_1} {S : Type u_2} [inst_1 : DecidableEq M] [inst_2 : AddCommMonoid M]
[inst_3 : SetLike S M] [inst_4 : AddSubmonoidClass S M] (A : ι → S) (x : DirectSum ι fun i => ↥(A i)),
(DirectSum.coeAddMonoidHom A) x = DFinsupp.sum x fun i x => ↑x- Defined in
- Mathlib.Algebra.DirectSum.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement · cited by 3,230
- SetLikestatement and proof · cited by 1,084
- DirectSumstatement and proof · cited by 446
- AddSubmonoidClassstatement and proof · cited by 346
- DFinsupp.sumstatement · cited by 64
- DFinsupp.sumAddHom_applyproof · cited by 16
- AddSubmonoidClass.subtypeproof · cited by 12
- DirectSum.coeAddMonoidHomstatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- HahnEmbedding.Seed.hahnCoeff_applyproof · cited by 1