Theorems · Theorem · group theory
DirectSum.decompose_symm_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).symm 0 = 0- Defined in
- Mathlib.Algebra.DirectSum.Decomposition
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
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
- Equiv.symmstatement · cited by 3,681
- map_zeroproof · cited by 1,614
- SetLikestatement and proof · cited by 1,084
- AddEquiv.symmproof · cited by 530
- 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
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