Theorems · Theorem · group theory
finprod_eq_prod
∀ {α : Type u_1} {M : Type u_5} [inst : CommMonoid M] (f : α → M) (hf : Function.HasFiniteMulSupport f),
∏ᶠ (i : α), f i = ∏ i ∈ Set.Finite.toFinset hf, f i- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Set.Finite.toFinsetstatement and proof · cited by 351
- finprodstatement · cited by 257
- Function.mulSupportstatement · cited by 240
- Function.HasFiniteMulSupportstatement and proof · cited by 99
- finprod_defproof · cited by 7
Cited by10
Results whose statement or proof uses this declaration.
- MeromorphicAt.finprodproof · cited by 5
- analyticAt_finprodproof · cited by 2
- meromorphicNFAt_finprodproof · cited by 1
- finprod_apply_ne_zeroproof · cited by 1
- mul_finprod_cond_neproof · cited by 1
- Topology.IsInducing.multipliable_iff_tprod_comp_mem_rangeproof · cited by 0
- finprod_eq_zeroproof · cited by 0
- tprod_le_of_prod_le'proof · cited by 0
- Function.FactorizedRational.ne_zeroproof · cited by 0
- meromorphicOrderAt_finprod_ne_topproof · cited by 0