Theorems · Theorem · order theory
ENat.prod_lt_top
∀ {α : Type u_1} {s : Finset α} {f : α → ℕ∞}, (∀ a ∈ s, f a < ⊤) → ∏ a ∈ s, f a < ⊤A product of finite numbers is still finite.
- Defined in
- Mathlib.Data.ENat.BigOperators
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- Top.topstatement and proof · cited by 9,680
- ENatstatement and proof · cited by 4,985
- Finset.prodstatement · cited by 2,356
- WithTop.prod_lt_topproof · cited by 2
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