Theorems · Theorem · linear algebra
Finsupp.single_mem_supported
∀ {α : Type u_1} {M : Type u_2} (R : Type u_5) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{s : Set α} {a : α} (b : M), a ∈ s → (fun₀ | a => b) ∈ Finsupp.supported M R s- Defined in
- Mathlib.LinearAlgebra.Finsupp.Supported
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement · cited by 7,192
- Finsuppstatement · cited by 5,255
- Finsupp.singlestatement · cited by 943
- Set.Subset.transproof · cited by 218
- Finsupp.supportedstatement · cited by 77
- Finsupp.support_single_subsetproof · cited by 27
- Finset.singleton_subset_set_iffproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Finsupp.span_image_eq_map_linearCombinationproof · cited by 7
- Finsupp.supported_eq_span_singleproof · cited by 3
- Submodule.set_smul_eq_mapproof · cited by 1
- Finsupp.supported_iUnionproof · cited by 1
- Finsupp.disjoint_supported_supported_iffproof · cited by 0