Theorems · Theorem · group theory
AddMonoidHom.map_finsum_of_injective
∀ {M : Type u_2} {N : Type u_3} {α : Sort u_4} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid N] (g : M →+ N),
Function.Injective ⇑g → ∀ (f : α → M), g (∑ᶠ (i : α), f i) = ∑ᶠ (i : α), g (f i)- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement and proof · cited by 3,230
- finsumstatement · cited by 286
- AddMonoidHom.map_zeroproof · cited by 47
- AddMonoidHom.map_finsum_of_preimage_zeroproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- Topology.IsClosedEmbedding.map_tsumproof · cited by 6
- AddEquiv.map_finsumproof · cited by 3
- finsum_smulproof · cited by 0
- smul_finsumproof · cited by 0