Theorems · Theorem · linear algebra
Finsupp.lapply_comp_lsingle_same
∀ {α : Type u_1} {M : Type u_2} {R : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(a : α), Finsupp.lapply a ∘ₗ Finsupp.lsingle a = LinearMap.id- Defined in
- Mathlib.LinearAlgebra.Finsupp.Defs
- Cited by
- 1 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Finsuppstatement · cited by 5,255
- LinearMap.compstatement · cited by 1,642
- LinearMap.extproof · cited by 844
- LinearMap.idstatement · cited by 625
- Finsupp.single_eq_sameproof · cited by 171
- Finsupp.lsinglestatement · cited by 75
- Finsupp.lapplystatement · cited by 19
Cited by1
Results whose statement or proof uses this declaration.
- Finsupp.comul_comp_lapplyproof · cited by 0