Theorems · Theorem · order theory
eq_bot_mono
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderBot α] {a b : α}, b ≤ a → a = ⊥ → b = ⊥- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PartialOrderOrderBot
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.
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- bot_uniqueproof · cited by 57
Cited by17
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_mono_nullproof · cited by 81
- MeasureTheory.tendsto_smul_aeproof · cited by 2
- MeasureTheory.tendsto_vadd_aeproof · cited by 2
- Set.Intersecting.isUpperSet'proof · cited by 2
- Dynamics.coverEntropyInfEntourage_emptyproof · cited by 1
- MeasureTheory.setLIntegral_eq_top_of_measure_eq_top_ne_zeroproof · cited by 1
- MeasureTheory.FiniteMeasure.mono_nullproof · cited by 1
- Polynomial.Sequence.linearIndependentproof · cited by 1
- bergelson'proof · cited by 1
- MeasureTheory.measure_preimage_smul_nullproof · cited by 0
- nhdsKer_eq_emptyproof · cited by 0
- MeasureTheory.measure_preimage_vadd_nullproof · cited by 0