Theorems · Theorem · order theory
lt_top_iff_ne_top
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderTop α] {a : α}, a < ⊤ ↔ a ≠ ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 95 results in Mathlib
- Foundations
- Depth 8 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
- LE.le.lt_iff_neproof · cited by 34
Cited by95
Results whose statement or proof uses this declaration.
- Ne.lt_topproof · cited by 161
- ENNReal.toReal_posproof · cited by 59
- MeasureTheory.integrableOn_constproof · cited by 15
- ENNReal.rpow_lt_top_of_nonnegproof · cited by 14
- ENNReal.tsum_geometricproof · cited by 8
- MeasureTheory.integrableOn_const_iffproof · cited by 7
- bot_lt_topproof · cited by 7
- MeasureTheory.stoppedProcess_stoppedProcessproof · cited by 6
- Ideal.ramificationIdx_posproof · cited by 5
- MeasureTheory.ofReal_integral_norm_eq_lintegral_enormproof · cited by 5
- MeasureTheory.Measure.count_apply_lt_topproof · cited by 4
- Set.encard_eq_top_iffproof · cited by 4