Theorems · Theorem · combinatorics
Finset.pi_nonempty
∀ {α : Type u_1} {β : α → Type u} {s : Finset α} {t : (a : α) → Finset (β a)} [inst : DecidableEq α],
(s.pi t).Nonempty ↔ ∀ a ∈ s, (t a).Nonempty- Defined in
- Mathlib.Data.Finset.Pi
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- Finset.Nonemptystatement · cited by 1,001
- Finset.pistatement · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Finset.pi_eq_emptyproof · cited by 0
- Finset.pi_nonempty_of_forall_nonemptyproof · cited by 0