Theorems · Theorem · combinatorics
Finset.Nonempty.product
∀ {α : Type u_1} {β : Type u_2} {s : Finset α} {t : Finset β}, s.Nonempty → t.Nonempty → (s ×ˢ t).Nonempty- Defined in
- Mathlib.Data.Finset.Prod
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- SProd.sprodstatement and proof · cited by 1,750
- Finset.Nonemptystatement and proof · cited by 1,001
- Finset.mem_productproof · cited by 48
Cited by11
Results whose statement or proof uses this declaration.
- Finset.prodMk_inf'_inf'statement and proof · cited by 2
- Finset.prodMk_sup'_sup'statement and proof · cited by 2
- Finset.inf'_sup_inf'statement and proof · cited by 2
- Finset.sup'_inf_sup'statement and proof · cited by 2
- Finset.truncatedSup_infsproof · cited by 1
- InfClosed.supClosureproof · cited by 1
- supClosure_prodproof · cited by 1
- infClosure_prodproof · cited by 1
- Finset.nonempty_productproof · cited by 1
- Finset.truncatedInf_supsproof · cited by 1
- SupClosed.infClosureproof · cited by 1