Theorems · Theorem · ring theory
GradedRing.mem_support_iff
∀ {ι : Type u_1} {A : Type u_3} {σ : Type u_4} [inst : DecidableEq ι] [inst_1 : AddMonoid ι] [inst_2 : Semiring A]
[inst_3 : SetLike σ A] [inst_4 : AddSubmonoidClass σ A] (𝒜 : ι → σ) [inst_5 : GradedRing 𝒜]
[inst_6 : (i : ι) → (x : ↥(𝒜 i)) → Decidable (x ≠ 0)] (r : A) (i : ι),
i ∈ DFinsupp.support ((DirectSum.decompose 𝒜) r) ↔ (GradedRing.proj 𝒜 i) r ≠ 0- Defined in
- Mathlib.RingTheory.GradedAlgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Finsetstatement · cited by 13,712
- Equivstatement · cited by 8,337
- AddMonoidHomstatement · cited by 3,230
- AddMonoidstatement and proof · cited by 2,864
- SetLikestatement and proof · cited by 1,084
- Iff.notproof · cited by 489
- DirectSumstatement · cited by 446
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- DFinsupp.supportstatement · cited by 158
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