Theorems · Theorem · order theory
Ne.lt_top
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderTop α] {a : α}, a ≠ ⊤ → a < ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 161 results in Mathlib
- Foundations
- Depth 9 from the axioms, rests on 20 definitions · uses no axioms
- Assumes
- PartialOrderOrderTop
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.
- Top.topstatement and proof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- lt_top_iff_ne_topproof · cited by 95
Cited by161
Results whose statement or proof uses this declaration.
- ne_top_of_le_ne_topproof · cited by 68
- MeasureTheory.MemLp.of_le_mulproof · cited by 7
- MeasureTheory.measure_le_setAverage_posproof · cited by 5
- MeasureTheory.MemLp.of_leproof · cited by 5
- MeasureTheory.setToFun_congr_measure_of_integrableproof · cited by 5
- nhds_top_basisproof · cited by 5
- Ideal.height_lt_topproof · cited by 4
- ProbabilityTheory.Fernique.logRatio_posproof · cited by 4
- MeasureTheory.measure_ball_lt_topproof · cited by 4
- ENNReal.div_lt_topproof · cited by 4
- MeasureTheory.measure_union_ne_topproof · cited by 4
- IsArtinian.surjective_of_injective_endomorphismproof · cited by 4