Theorems · Theorem · order theory
bot_lt_iff_ne_bot
∀ {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 8 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 · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- bot_leproof · cited by 306
- LE.le.lt_iff_ne'proof · cited by 16
Cited by57
Results whose statement or proof uses this declaration.
- Ne.bot_ltproof · cited by 116
- ENNReal.toReal_posproof · cited by 59
- Polynomial.degree_lt_degreeproof · cited by 14
- MeasureTheory.Measure.addHaar_smulproof · cited by 13
- Polynomial.degree_derivative_ltproof · cited by 4
- LinearMap.det_eq_zero_iff_ker_ne_botproof · cited by 3
- MeasureTheory.exists_eLpNorm_indicator_leproof · cited by 3
- Ideal.mul_iInfproof · cited by 3
- Ring.not_isField_iff_exists_ideal_bot_lt_and_lt_topproof · cited by 3
- bot_lt_isotypicComponentproof · cited by 3
- not_bot_lt_iffproof · cited by 2
- FractionalIdeal.exists_ne_zero_mem_isIntegerproof · cited by 2