Theorems · Theorem · order theory
not_top_lt
∀ {α : Type u} [inst : Preorder α] [inst_1 : OrderTop α] {a : α}, ¬⊤ < a- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 17 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.
- Top.topstatement · cited by 9,680
- Preorderstatement and proof · cited by 7,952
- OrderTopstatement and proof · cited by 493
- isMax_topproof · cited by 12
- IsMax.not_ltproof · cited by 8
Cited by17
Results whose statement or proof uses this declaration.
- EReal.exists_rat_btwn_of_ltproof · cited by 5
- WithTop.strictMono_iffproof · cited by 4
- EReal.exp_strictMonoproof · cited by 3
- EReal.exists_between_coe_realproof · cited by 3
- EReal.mul_bot_of_negproof · cited by 2
- HahnSeries.orderTop_smul_not_ltproof · cited by 2
- LinearGrowth.EReal.eventually_atTop_exists_nat_betweenproof · cited by 2
- EReal.mul_top_of_negproof · cited by 1
- Finset.inf_lt_iffproof · cited by 1
- AffineSubspace.inter_nonempty_of_nonempty_of_sup_direction_eq_topproof · cited by 1
- not_top_covByproof · cited by 0
- WithTop.exists_lt_coeproof · cited by 0