Theorems · Theorem · group theory
AddMonoidHom.map_finsum
∀ {α : Type u_1} {M : Type u_5} {N : Type u_6} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid N] {f : α → M}
(g : M →+ N), Function.HasFiniteSupport f → g (∑ᶠ (i : α), f i) = ∑ᶠ (i : α), g (f i)- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 75 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddMonoidHomstatement and proof · cited by 3,230
- Equiv.injectiveproof · cited by 464
- finsumstatement · cited by 286
- Function.Injective.injOnproof · cited by 280
- Function.HasFiniteSupportstatement and proof · cited by 113
- Equiv.pliftproof · cited by 23
- Set.Finite.preimageproof · cited by 16
- AddMonoidHom.map_finsum_pliftproof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- MvPowerSeries.map_substproof · cited by 2
- AddMonoidHom.map_finsum_mem'proof · cited by 1
- map_finsumproof · cited by 1
- finsum_mul'proof · cited by 1
- mul_finsum'proof · cited by 1
- finsum_smul'proof · cited by 0
- smul_finsum'proof · cited by 0
- finsum_nsmulproof · cited by 0
- Nat.cast_finsumproof · cited by 0