Theorems · Theorem · order theory
Order.Ideal.nonempty
∀ {P : Type u_1} [inst : LE P] (s : Order.Ideal P), (↑s).Nonempty- Defined in
- Mathlib.Order.Ideal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- LE
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.
- SetLike.coestatement · cited by 8,199
- Set.Nonemptystatement · cited by 2,627
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.nonempty'proof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Order.PFilter.nonemptyproof · cited by 4
- Order.Ideal.isIdealproof · cited by 3
- Order.Ideal.inter_nonemptyproof · cited by 0