Theorems · Theorem · order theory
WithTop.eq_bot_iff_forall_le
∀ {α : Type u_1} [inst : PartialOrder α] [Nonempty α] [NoBotOrder α] {x : WithTop (WithBot α)},
x = ⊥ ↔ ∀ (a : α), x ≤ ↑↑a- Defined in
- Mathlib.Order.WithBot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topproof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- WithTopstatement and proof · cited by 3,754
- WithBotstatement and proof · cited by 1,498
- WithTop.somestatement and proof · cited by 1,128
- WithBot.somestatement and proof · cited by 541
- bot_leproof · cited by 306
- top_le_iffproof · cited by 175
- WithTop.recTopCoeproof · cited by 107
- WithTop.coe_le_coeproof · cited by 65
- NoBotOrderstatement and proof · cited by 43
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