Theorems · Theorem · order theory
Order.not_isSuccPrelimit_succ
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] [NoMaxOrder α] (a : α), ¬Order.IsSuccPrelimit (Order.succ a)- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 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.
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
- 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
- Order.IsSuccPrelimit.succ_neproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Order.IsSuccPrelimit.isMin_of_noMaxproof · cited by 2
- Order.not_isSuccPrelimit_add_oneproof · cited by 0