Mathlib Map

Theorems · Theorem · combinatorics

Set.infinite_prod

∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : Set β},
  (s ×ˢ t).Infinite ↔ s.Infinite ∧ t.Nonempty ∨ t.Infinite ∧ s.Nonempty
Defined in
Mathlib.Data.Finite.Prod
Cited by
2 results in Mathlib
Foundations
Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.infinite_image2 · cited by 5Set.infinite_image2Set.finite_prod · cited by 0Set.finite_prodSet · cited by 53352SetSet.Nonempty · cited by 2627Set.NonemptySet.Finite · cited by 1814Set.FiniteSProd.sprod · cited by 1750SProd.sprodSet.Infinite · cited by 263Set.InfiniteSet.Finite.prod · cited by 9Finite.prodSet.Infinite.nonempty · cited by 6Infinite.nonemptySet.Nonempty.fst · cited by 4Nonempty.fstSet.Nonempty.snd · cited by 4Nonempty.sndSet.Infinite.prod_left · cited by 1Infinite.prod_leftSet.Infinite.prod_right · cited by 1Infinite.prod_rightSet.infinite_prodCITED BYCITES

Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.