Theorems · Theorem · order theory
directedOn_pair
∀ {α : Type u_1} {r : α → α → Prop} [Std.Refl r] {a b : α}, r a b → DirectedOn r {a, b}- Defined in
- Mathlib.Order.Directed
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- Std.Refl
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- DirectedOnstatement · cited by 271
- reflproof · cited by 80
- directedOn_singletonproof · cited by 2
- DirectedOn.insertproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- ScottContinuousOn.monotoneproof · cited by 5
- directedOn_pair'proof · cited by 0