Theorems · Theorem · group theory
finprod_eq_finsetProd_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
- 7 results in Mathlib
- Foundations
- Depth 76 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Finset.prodstatement · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Set.Finite.subsetproof · cited by 285
- finprodstatement · cited by 257
- Function.mulSupportstatement and proof · cited by 240
- Finset.finite_toSetproof · cited by 210
- Set.Finite.coe_toFinsetproof · cited by 124
- finprod_eq_prod_of_mulSupport_toFinset_subsetproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- finprod_le_finprodproof · cited by 5
- Ideal.map_algebraMap_eq_finsetProd_powproof · cited by 2
- IsDedekindDomain.isOpen_of_ne_botproof · cited by 1
- finprod_le_finprod'proof · cited by 0
- finprod_prod_filterproof · cited by 0
- FractionalIdeal.count_finprodproof · cited by 0
- finprod_eq_finset_prod_of_mulSupport_subsetproof · cited by 0