Theorems · Theorem · order theory
Order.not_isSuccLimit_iff
∀ {α : Type u_1} {a : α} [inst : Preorder α], ¬Order.IsSuccLimit a ↔ IsMin a ∨ ¬Order.IsSuccPrelimit a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 13 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.
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
- IsMinstatement and proof · cited by 277
- Order.IsSuccLimitstatement · cited by 255
- Order.IsSuccPrelimitstatement and proof · cited by 157
- not_and_orproof · cited by 82
- Order.isSuccLimit_iffproof · cited by 9
Cited by1
Results whose statement or proof uses this declaration.
- SuccOrder.isOpen_singleton_iffproof · cited by 3