Theorems · Theorem · order theory
Order.Ideal.directed
∀ {P : Type u_1} [inst : LE P] (s : Order.Ideal P), DirectedOn (fun x1 x2 => x1 ≤ x2) ↑s- Defined in
- Mathlib.Order.Ideal
- Cited by
- 5 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
- DirectedOnstatement · cited by 271
- Order.Idealstatement and proof · cited by 102
- Order.Ideal.directed'proof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- Order.Ideal.sup_memproof · cited by 5
- Order.Ideal.isIdealproof · cited by 3
- Order.iso_of_countable_denseproof · cited by 0
- Order.embedding_from_countable_to_denseproof · cited by 0
- Order.PFilter.directedproof · cited by 0