Theorems · Theorem · order theory
Order.IsSuccLimit.pos
∀ {α : Type u_1} {a : α} [inst : Preorder α] [inst_1 : Zero α] [IsBotZeroClass α], Order.IsSuccLimit a → 0 < a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderZeroIsBotZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- OrderBotproof · cited by 1,055
- Order.IsSuccLimitstatement and proof · cited by 255
- IsBotZeroClassstatement and proof · cited by 71
- Order.IsSuccLimit.bot_ltproof · cited by 13
- IsBotZeroClass.toOrderBotproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Ordinal.opow_posproof · cited by 22
- Order.IsSuccLimit.natCast_ltproof · cited by 1
- Order.IsSuccLimit.ne_zeroproof · cited by 0