Theorems · Theorem · order theory
Order.IsSuccLimit.bot_lt
∀ {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
- 13 results in Mathlib
- Foundations
- Depth 16 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
- OrderBotstatement and proof · cited by 1,055
- Order.IsSuccLimitstatement and proof · cited by 255
- Order.IsSuccLimit.not_isMinproof · cited by 15
- not_isMin_iff_bot_ltproof · cited by 1
Cited by13
Results whose statement or proof uses this declaration.
- Ordinal.one_opowproof · cited by 9
- Order.IsSuccLimit.ne_botproof · cited by 5
- Ordinal.natCast_lt_of_isSuccLimitproof · cited by 3
- Order.IsSuccLimit.posproof · cited by 3
- Ordinal.isSuccLimit_opow_leftproof · cited by 1
- OrdinalApprox.lfpApprox_of_isSuccLimitproof · cited by 1
- Ordinal.isNormal_veblenWith_zeroproof · cited by 1
- Ordinal.isSuccLimit_mul_leftproof · cited by 1
- Profinite.NobelingProof.Products.limitOrdinalproof · cited by 1
- Ordinal.isNormal_enumOrdproof · cited by 0
- CategoryTheory.SmallObject.SuccStruct.Iteration.obj_limitproof · cited by 0
- SSet.Subcomplex.Pairing.RankFunction.filtration_of_isSuccLimitproof · cited by 0