Theorems · Theorem · linear algebra
DFinsupp.lapply_comp_lsingle_same
∀ {ι : Type u_1} {R : Type u_3} {M : ι → Type u_5} [inst : Semiring R] [inst_1 : (i : ι) → AddCommMonoid (M i)]
[inst_2 : (i : ι) → Module R (M i)] [inst_3 : DecidableEq ι] (i : ι),
DFinsupp.lapply i ∘ₗ DFinsupp.lsingle i = LinearMap.id- Defined in
- Mathlib.LinearAlgebra.DFinsupp
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
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
- LinearMap.compstatement · cited by 1,642
- LinearMap.extproof · cited by 844
- DFinsuppstatement · cited by 694
- LinearMap.idstatement · cited by 625
- DFinsupp.single_applyproof · cited by 35
- DFinsupp.lsinglestatement · cited by 23
- DFinsupp.lapplystatement · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- DFinsupp.comul_comp_lapplyproof · cited by 0