Theorems · Theorem · order theory
zero_notMem_iff
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : Zero α] [IsBotZeroClass α] {s : Set α}, 0 ∉ s ↔ ∀ x ∈ s, 0 < x- Defined in
- Mathlib.Algebra.Order.IsBotOne
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
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Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- OrderBotproof · cited by 1,055
- IsBotZeroClassstatement and proof · cited by 71
- IsBotZeroClass.toOrderBotproof · cited by 4
- bot_notMem_iffproof · cited by 2
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