Theorems · Theorem · order theory
PredOrder.forall_ne_top_iff
∀ {α : Type u_1} [Nontrivial α] [inst : PartialOrder α] [inst_1 : OrderTop α] [inst_2 : PredOrder α]
[IsPredArchimedean α] (P : α → Prop), (∀ (i : α), i ≠ ⊤ → P i) ↔ ∀ (i : α), P (PredOrder.pred i)- Defined in
- Mathlib.Order.SuccPred.Archimedean
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- Nontrivialstatement and proof · cited by 2,416
- Nat.iterateproof · cited by 740
- OrderTopstatement and proof · cited by 493
- le_topproof · cited by 411
- PredOrderstatement and proof · cited by 334
- Order.predproof · cited by 273
- IsPredArchimedeanstatement and proof · cited by 66
- Function.iterate_succ'proof · cited by 56
- IsPredArchimedean.exists_pred_iterate_of_leproof · cited by 11
- PredOrder.predstatement and proof · cited by 8
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