Theorems · Theorem · group theory
finprod_of_not_hasFiniteMulSupport
∀ {α : Type u_1} {M : Type u_5} [inst : CommMonoid M] {f : α → M}, ¬Function.HasFiniteMulSupport f → ∏ᶠ (i : α), f i = 1- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 83 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
- finprodstatement · cited by 257
- Function.HasFiniteMulSupportstatement and proof · cited by 99
- finprod_of_infinite_mulSupportproof · cited by 13
- Set.not_finiteproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- MeromorphicAt.finprodproof · cited by 5
- meromorphicNFAt_finprodproof · cited by 1
- finprod_zero_le_oneproof · cited by 1
- meromorphicOrderAt_finprod_ne_topproof · cited by 0
- Nat.cast_finprod'proof · cited by 0