Theorems · Theorem · group theory
one_lt_finprod
∀ {ι : Type u_3} {M : Type u_7} [inst : CommMonoid M] [inst_1 : PartialOrder M] [IsOrderedCancelMonoid M] {f : ι → M},
(∀ (i : ι), 1 ≤ f i) → (∃ i, 1 < f i) → Function.HasFiniteMulSupport f → 1 < ∏ᶠ (i : ι), f i- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredproof · cited by 6,101
- CommMonoidstatement and proof · cited by 2,264
- Set.Finiteproof · cited by 1,814
- finprodstatement · cited by 257
- Function.mulSupportproof · cited by 240
- Set.inter_univproof · cited by 198
- Function.HasFiniteMulSupportstatement and proof · cited by 99
- IsOrderedCancelMonoidstatement and proof · cited by 65
- finprod_mem_univproof · cited by 3
- one_lt_finprod_condproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- one_lt_finprod'proof · cited by 0