Theorems · Theorem · linear algebra
LinearMap.map_dfinsuppSumAddHom
∀ {R : Type u_7} {R₂ : Type u_8} {M : Type u_9} {M₂ : Type u_10} {ι : Type u_11} [inst : Semiring R]
[inst_1 : Semiring R₂] [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {σ₁₂ : R →+* R₂} [inst_4 : Module R M]
[inst_5 : Module R₂ M₂] {γ : ι → Type u_12} [inst_6 : DecidableEq ι] [inst_7 : (i : ι) → AddZeroClass (γ i)]
(f : M →ₛₗ[σ₁₂] M₂) {t : Π₀ (i : ι), γ i} {g : (i : ι) → γ i →+ M},
f ((DFinsupp.sumAddHom g) t) = (DFinsupp.sumAddHom fun i => f.toAddMonoidHom.comp (g i)) t- Defined in
- Mathlib.LinearAlgebra.DFinsupp
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- AddMonoidHomstatement and proof · cited by 3,230
- AddZeroClassstatement and proof · cited by 1,237
- DFinsuppstatement and proof · cited by 694
- AddMonoidHom.compstatement · cited by 339
- LinearMap.toAddMonoidHomstatement and proof · cited by 101
- DFinsupp.sumAddHomstatement · cited by 38
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