Theorems · Theorem · order theory
Sublattice.pi_univ_eq_bot_iff
∀ {κ : Type u_5} {π : κ → Type u_6} [inst : (i : κ) → Lattice (π i)] {L : (i : κ) → Sublattice (π i)},
Sublattice.pi Set.univ L = ⊥ ↔ ∃ i, L i = ⊥- Defined in
- Mathlib.Order.Sublattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Lattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement and proof · cited by 4,720
- Set.univstatement and proof · cited by 3,945
- Latticestatement and proof · cited by 916
- Sublatticestatement and proof · cited by 225
- Sublattice.pistatement · cited by 9
- Sublattice.coe_piproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Sublattice.pi_univ_eq_botproof · cited by 0