Theorems · Theorem · order theory
ne_top_of_lt
∀ {α : Type u} [inst : Preorder α] [inst_1 : OrderTop α] {a b : α}, a < b → a ≠ ⊤- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
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.
Cited by50
Results whose statement or proof uses this declaration.
- LT.lt.ne_topproof · cited by 34
- ENNReal.le_of_forall_nnreal_ltproof · cited by 16
- ENNReal.strictMono_rpow_of_posproof · cited by 7
- MeasureTheory.AECover.integrable_of_integral_norm_boundedproof · cited by 6
- thickenedIndicator_le_oneproof · cited by 5
- ENNReal.iUnion_Iio_coe_natproof · cited by 4
- MeasureTheory.eLpNorm_le_eLpNorm_mul_eLpNorm_of_nnnormproof · cited by 4
- ProbabilityTheory.Fernique.logRatio_posproof · cited by 4
- MeasureTheory.IsStoppingTime.measurableSet_eq_of_countable_rangeproof · cited by 4
- HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principalproof · cited by 3
- MvPowerSeries.nat_le_weightedOrderproof · cited by 3
- MeasureTheory.Measure.hausdorffMeasure_zero_or_topproof · cited by 3