Theorems · Theorem · order theory
bot_unique
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderBot α] {a : α}, a ≤ ⊥ → a = ⊥- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 57 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PartialOrderOrderBot
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.
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- bot_leproof · cited by 306
- LE.le.antisymm'proof · cited by 104
Cited by57
Results whose statement or proof uses this declaration.
- Disjoint.eq_botproof · cited by 52
- ENNReal.inv_topproof · cited by 36
- iSup_botproof · cited by 29
- disjoint_selfproof · cited by 28
- MeasureTheory.Measure.measure_univ_eq_zeroproof · cited by 26
- Filter.principal_emptyproof · cited by 19
- Filter.empty_mem_iff_botproof · cited by 18
- eq_bot_monoproof · cited by 17
- MonoidHom.ker_eq_bot_iffproof · cited by 16
- AddMonoidHom.ker_eq_bot_iffproof · cited by 14
- sSup_eq_botproof · cited by 7
- Submonoid.powers_oneproof · cited by 7