Theorems · Theorem · order theory
Order.IsSuccPrelimit.succ_ne
∀ {α : Type u_1} {a : α} [inst : Preorder α] [inst_1 : SuccOrder α] [NoMaxOrder α],
Order.IsSuccPrelimit a → ∀ (b : α), Order.succ b ≠ a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderSuccOrderNoMaxOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- NoMaxOrderstatement and proof · cited by 340
- Order.IsSuccPrelimitstatement and proof · cited by 157
- not_isMaxproof · cited by 46
- Order.IsSuccPrelimit.isMaxproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Order.not_isSuccPrelimit_succproof · cited by 2
- Order.IsSuccLimit.succ_neproof · cited by 1
- Order.isSuccPrelimit_iff_succ_neproof · cited by 1