Theorems · Theorem · linear algebra
Finsupp.supported_iUnion
∀ {α : Type u_1} {M : Type u_2} {R : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{δ : Type u_7} (s : δ → Set α), Finsupp.supported M R (⋃ i, s i) = ⨆ i, Finsupp.supported M R (s i)- Defined in
- Mathlib.LinearAlgebra.Finsupp.Supported
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 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.
Cites36
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
- Top.topproof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- Finsuppstatement and proof · cited by 5,255
- Set.iUnionstatement and proof · cited by 2,483
- iSupstatement and proof · cited by 2,415
- le_antisymmproof · cited by 2,068
- LinearMap.compproof · cited by 1,642
- Finsupp.singleproof · cited by 943
Cited by1
Results whose statement or proof uses this declaration.
- Finsupp.supported_unionproof · cited by 2