Theorems · Theorem · group theory
DirectSum.degree_eq_of_mem_mem
∀ {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) [DirectSum.Decomposition ℳ] {x : M} {i j : ι},
x ∈ ℳ i → x ∈ ℳ j → x ≠ 0 → i = j- Defined in
- Mathlib.Algebra.DirectSum.Decomposition
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- AddCommMonoidstatement and proof · cited by 12,281
- SetLikestatement and proof · cited by 1,084
- AddSubmonoidClassstatement and proof · cited by 346
- DirectSum.Decompositionstatement and proof · cited by 57
- DirectSum.decompose_of_mem_neproof · cited by 7
- DirectSum.decompose_of_mem_sameproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- HomogeneousLocalization.Away.mk_surjectiveproof · cited by 2
- HomogeneousLocalization.Away.span_mk_prod_pow_eq_topproof · cited by 1
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.num_mem_carrier_iffproof · cited by 1
- AlgebraicGeometry.Proj.lift_awayMapₐ_awayMapₐ_surjectiveproof · cited by 0
- HomogeneousLocalization.Away.eventually_smul_memproof · cited by 0