Theorems · Theorem · linear algebra
Submodule.image_smul_top_eq_range_lsum
∀ {R : Type u_1} {M : Type u_2} {σ : Type u_4} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(s : Set σ) (f : σ → R), f '' s • ⊤ = ((Finsupp.lsum R) fun i => f ↑i • LinearMap.id).range- Defined in
- Mathlib.LinearAlgebra.Finsupp.Span
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Set.Elemstatement and proof · cited by 7,166
- Set.imagestatement and proof · cited by 5,609
- Finsuppstatement · cited by 5,255
Cited by2
Results whose statement or proof uses this declaration.
- AdicCompletion.pow_smul_top_eq_ker_evalproof · cited by 4
- Submodule.smul_top_eq_range_lsumproof · cited by 1