Theorems · Theorem · order theory
not_lt_bot
∀ {α : Type u} [inst : Preorder α] [inst_1 : OrderBot α] {a : α}, ¬a < ⊥- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
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.
- Preorderstatement and proof · cited by 7,952
- Bot.botstatement · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- isMin_botproof · cited by 15
- IsMin.not_ltproof · cited by 8
Cited by19
Results whose statement or proof uses this declaration.
- EReal.mul_bot_of_posproof · cited by 7
- Polynomial.natDegree_lt_natDegreeproof · cited by 5
- EReal.mul_top_of_posproof · cited by 4
- EReal.exists_between_coe_realproof · cited by 3
- not_covBy_botproof · cited by 2
- Nat.WithBot.one_le_iff_zero_ltproof · cited by 2
- LinearGrowth.EReal.eventually_atTop_exists_nat_betweenproof · cited by 2
- EReal.inv_strictAntiOnproof · cited by 2
- WithBot.strictMono_iffproof · cited by 2
- Nat.WithBot.add_one_le_of_ltproof · cited by 1
- WithBot.covBy_bot_iffproof · cited by 1
- Polynomial.exists_degree_le_of_mem_spanproof · cited by 1