Theorems · Theorem · order theory
LowerSet.lower
∀ {α : Type u_1} [inst : LE α] (s : LowerSet α), IsLowerSet ↑s- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 10 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
- LowerSetstatement and proof · cited by 230
- IsLowerSetstatement · cited by 167
- LowerSet.lower'proof · cited by 3
Cited by13
Results whose statement or proof uses this declaration.
- lowerClosure_leproof · cited by 3
- Topology.IsUpperSet.closure_eq_lowerClosureproof · cited by 3
- LowerSet.sdiff_eq_leftproof · cited by 2
- Set.OrdConnected.null_frontierproof · cited by 2
- LowerSet.Iic_leproof · cited by 1
- lowerClosure_eqproof · cited by 0
- Set.OrdConnected.vaddproof · cited by 0
- lowerClosure_interior_subsetproof · cited by 0
- lowerClosure_interior_subset'proof · cited by 0
- ordConnected_iff_upperClosure_inter_lowerClosureproof · cited by 0
- closure_lowerClosure_comm_piproof · cited by 0
- Set.OrdConnected.smulproof · cited by 0