Theorems · Theorem · group theory
finprod_of_infinite_mulSupport
∀ {α : Type u_1} {M : Type u_5} [inst : CommMonoid M] {f : α → M},
(Function.mulSupport f).Infinite → ∏ᶠ (i : α), f i = 1- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 13 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- Set.Infinitestatement and proof · cited by 263
- finprodstatement · cited by 257
- Function.mulSupportstatement and proof · cited by 240
- finprod_defproof · cited by 7
Cited by13
Results whose statement or proof uses this declaration.
- tprod_botproof · cited by 6
- finprod_of_not_hasFiniteMulSupportproof · cited by 5
- MeromorphicOn.extract_zeros_poles_logproof · cited by 3
- Function.FactorizedRational.meromorphicNFOn_univproof · cited by 3
- Function.FactorizedRational.meromorphicOrderAt_ne_topproof · cited by 2
- analyticAt_finprodproof · cited by 2
- hasFiniteMulSupport_of_finprod_ne_oneproof · cited by 1
- finprod_apply_ne_zeroproof · cited by 1
- finprod_mem_eq_one_of_infiniteproof · cited by 1
- Topology.IsInducing.multipliable_iff_tprod_comp_mem_rangeproof · cited by 0
- tprod_le_of_prod_le'proof · cited by 0
- finprod_ne_zeroproof · cited by 0