Theorems · Theorem · order theory
LowerSet.Iic_le
∀ {α : Type u_1} [inst : Preorder α] {s : LowerSet α} {a : α}, LowerSet.Iic a ≤ s ↔ a ∈ s- Defined in
- Mathlib.Order.UpperLower.Principal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- le_rflproof · cited by 1,558
- LowerSetstatement and proof · cited by 230
- LowerSet.Iicstatement and proof · cited by 37
- LowerSet.lowerproof · cited by 13
- IsLowerSet.Iic_subsetproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- LowerSet.supIrred_Iicproof · cited by 4