Theorems · Theorem · ring theory
MonoidAlgebra.mem_supported
∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : Module R S]
{s : Set M} {x : MonoidAlgebra S M}, x ∈ MonoidAlgebra.supported R S s ↔ ↑x.coeff.support ⊆ s- Defined in
- Mathlib.Algebra.MonoidAlgebra.Module
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- Finsetstatement · cited by 13,712
- SetLike.coestatement · cited by 8,199
- Submodulestatement · cited by 7,192
- Finsupp.supportstatement · cited by 828
- MonoidAlgebrastatement and proof · cited by 590
- MonoidAlgebra.coeffstatement · cited by 224
- MonoidAlgebra.supportedstatement · cited by 9
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