Theorems · Theorem · order theory
not_bot_lt_iff
∀ {α : Type u} [inst : PartialOrder α] [inst_1 : OrderBot α] {a : α}, ¬⊥ < a ↔ a = ⊥- Defined in
- Mathlib.Order.BoundedOrder.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- 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_lt_iff_ne_botproof · cited by 57
- Iff.not_leftproof · cited by 49
Cited by2
Results whose statement or proof uses this declaration.
- eq_bot_of_generator_maximal_submoduleImage_eq_zeroproof · cited by 1
- eq_bot_of_generator_maximal_map_eq_zeroproof · cited by 0