Theorems · Theorem · group theory
finprod_eq_prod_of_mulSupport_subset
∀ {α : Type u_1} {M : Type u_5} [inst : CommMonoid M] (f : α → M) {s : Finset α},
Function.mulSupport f ⊆ ↑s → ∏ᶠ (i : α), f i = ∏ i ∈ s, f i- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 74 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.imageproof · cited by 5,609
- Equiv.symmproof · cited by 3,681
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.mapproof · cited by 747
- Finset.prod_congrproof · cited by 646
- finprodstatement · cited by 257
- Equiv.toEmbeddingproof · cited by 254
Cited by21
Results whose statement or proof uses this declaration.
- Multipliable.hasProdproof · cited by 88
- finprod_mul_distribproof · cited by 8
- finprod_cond_eq_prod_of_cond_iffproof · cited by 6
- finprod_eq_prod_of_mulSupport_toFinset_subsetproof · cited by 6
- MeromorphicOn.extract_zeros_poles_logproof · cited by 3
- tprod_eq_prod'proof · cited by 3
- finprod_prod_commproof · cited by 3
- finprod_mem_finset_product'proof · cited by 2
- Function.FactorizedRational.extractFactorproof · cited by 2
- finprod_eventually_eq_prodproof · cited by 2
- Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAtproof · cited by 1