Theorems · Theorem · order theory
Order.IsPredLimit.withBotCoe
∀ {α : Type u_1} [inst : Preorder α] {x : α}, Order.IsPredLimit x → Order.IsPredLimit ↑x- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- WithBotstatement · cited by 1,498
- WithBot.somestatement and proof · cited by 541
- Order.IsPredLimitstatement and proof · cited by 60
- WithBot.coe_lt_coeproof · cited by 55
- not_isMax_iffproof · cited by 24
- Order.IsPredLimit.isPredPrelimitproof · cited by 23
- not_lt_botproof · cited by 19
- Order.IsPredLimit.not_isMaxproof · cited by 11
- Order.isPredLimit_iffproof · cited by 10
- WithBot.existsproof · cited by 3
- Order.IsPredPrelimit.withBotCoeproof · cited by 1
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