Theorems · Theorem · order theory
Order.IsSuccLimit.ne_bot
∀ {α : Type u_1} {a : α} [inst : Preorder α] [inst_1 : OrderBot α], Order.IsSuccLimit a → a ≠ ⊥- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Bot.botstatement · cited by 4,720
- LT.lt.ne'proof · cited by 1,417
- OrderBotstatement and proof · cited by 1,055
- Order.IsSuccLimitstatement and proof · cited by 255
- Order.IsSuccLimit.bot_ltproof · cited by 13
Cited by5
Results whose statement or proof uses this declaration.
- Ordinal.IsNormal.bsup_eqproof · cited by 2
- Ordinal.lt_add_iff_of_isSuccLimitproof · cited by 1
- Ordinal.isNormal_veblenWith_zeroproof · cited by 1
- Cardinal.ne_zero_of_isSuccLimitproof · cited by 0
- Order.isNormal_enum_iff_dirSupClosedproof · cited by 0