Theorems · Theorem · order theory
Order.max_of_succ_le
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a : α}, Order.succ a ≤ a → IsMax a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement · cited by 372
- SuccOrder.max_of_succ_leproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Order.succ_eq_iff_isMaxproof · cited by 11
- Order.succ_le_iff_isMaxproof · cited by 3
- Order.lt_succ_iff_not_isMaxproof · cited by 3
- Order.isMax_iterate_succ_of_eq_of_ltproof · cited by 2
- CategoryTheory.IsCardinalFiltered.exists_cardinal_directedproof · cited by 1
- Order.succ_eq_zeroproof · cited by 0