Theorems · Theorem · order theory
ne_top_of_le_ne_top
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderTop α] {a b : α}, b ≠ ⊤ → a ≤ b → a ≠ ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 68 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- PartialOrderOrderTop
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.
- Top.topstatement and proof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- LT.lt.neproof · cited by 872
- LE.le.trans_ltproof · cited by 795
- OrderTopstatement and proof · cited by 493
- Ne.lt_topproof · cited by 161
Cited by68
Results whose statement or proof uses this declaration.
- ENNReal.toReal_monoproof · cited by 59
- ENNReal.toReal_le_of_le_ofRealproof · cited by 14
- Metric.infEDist_ne_topproof · cited by 8
- AntilipschitzWith.isBounded_preimageproof · cited by 6
- ENNReal.toReal_sub_of_leproof · cited by 6
- MeasurableSet.exists_isCompact_isClosed_sdiff_ltproof · cited by 5
- Metric.isBounded_iff_ediam_ne_topproof · cited by 5
- ENat.toNat_le_of_le_natCastproof · cited by 5
- MeasureTheory.TendstoInMeasure.exists_seq_tendsto_aeproof · cited by 5
- Metric.hausdorffEDist_ne_top_of_nonempty_of_boundedproof · cited by 4
- Monotone.measure_iInterproof · cited by 4
- MeasurableSet.exists_isClosed_sdiff_ltproof · cited by 3