Theorems · Theorem · group theory
DirectSum.decompose_zero
∀ {ι : Type u_1} {M : Type u_3} {σ : Type u_4} [inst : DecidableEq ι] [inst_1 : AddCommMonoid M] [inst_2 : SetLike σ M]
[inst_3 : AddSubmonoidClass σ M] (ℳ : ι → σ) [inst_4 : DirectSum.Decomposition ℳ], (DirectSum.decompose ℳ) 0 = 0- Defined in
- Mathlib.Algebra.DirectSum.Decomposition
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 90 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
- Equivstatement · cited by 8,337
- map_zeroproof · cited by 1,614
- SetLikestatement and proof · cited by 1,084
- DirectSumstatement · cited by 446
- AddSubmonoidClassstatement and proof · cited by 346
- DirectSum.decomposestatement · cited by 93
- DirectSum.Decompositionstatement and proof · cited by 57
- DirectSum.decomposeAddEquivproof · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- IsHomogeneous.subsemiringClosureproof · cited by 1
- HomogeneousLocalization.Away.span_mk_prod_pow_eq_topproof · cited by 1
- Ideal.IsHomogeneous.botproof · cited by 0
- IsHomogeneous.subsemiringClosure_of_isHomogeneousElemproof · cited by 0