Theorems · Theorem · order theory
IsLowerSet.ordConnected
∀ {α : Type u_1} [inst : Preorder α] {s : Set α}, IsLowerSet s → s.OrdConnected- Defined in
- Mathlib.Order.UpperLower.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 57 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- LE.le.transproof · cited by 3,151
- IsLowerSetstatement and proof · cited by 167
- Set.OrdConnectedstatement · cited by 161
- Set.Icc_subset_Iic_selfproof · cited by 10
- IsLowerSet.Iic_subsetproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- InitialSeg.apply_covBy_apply_iffproof · cited by 4
- Set.OrdConnected.vaddproof · cited by 0
- Set.OrdConnected.smulproof · cited by 0
- ordConnected_iff_upperClosure_inter_lowerClosureproof · cited by 0
- Set.OrdConnected.interiorproof · cited by 0