Theorems · Theorem · order theory
Set.insert_nonempty
∀ {α : Type u_1} (a : α) (s : Set α), (insert a s).Nonempty- Defined in
- Mathlib.Data.Set.Insert
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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.
- Setstatement and proof · cited by 53,352
- Set.Nonemptystatement · cited by 2,627
- Set.mem_insertproof · cited by 109
Cited by13
Results whose statement or proof uses this declaration.
- ScottContinuousOn.monotoneproof · cited by 5
- CountableInfClosed.infClosedproof · cited by 3
- convexJoin_segmentsproof · cited by 2
- ContinuousOn.exists_isMinOn'proof · cited by 2
- MeasureTheory.Measure.inf_applyproof · cited by 2
- RightOrdContinuous.map_infproof · cited by 1
- exists_nonempty_countable_separatingproof · cited by 1
- LeftOrdContinuous.map_supproof · cited by 1
- csInf_insertproof · cited by 0
- csSup_pairproof · cited by 0
- csSup_insertproof · cited by 0
- csSup_insert'proof · cited by 0