Theorems · Theorem · order theory
LowerSet.mem_Iic_iff
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, b ∈ LowerSet.Iic a ↔ b ≤ a- Defined in
- Mathlib.Order.UpperLower.Principal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- LowerSetstatement · cited by 230
- LowerSet.Iicstatement · cited by 37
Cited by3
Results whose statement or proof uses this declaration.
- LowerSet.supIrred_Iicproof · cited by 4
- LowerSet.Iic_iInfproof · cited by 1
- LowerSet.Iic_sInfproof · cited by 0