Theorems · Theorem · order theory
Order.isMax_iterate_succ_of_eq_of_ne
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a : α} {n m : ℕ},
Order.succ^[n] a = Order.succ^[m] a → n ≠ m → IsMax (Order.succ^[n] a)- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Nat.iteratestatement and proof · cited by 740
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- le_totalproof · cited by 294
- lt_of_le_of_neproof · cited by 230
- Order.isMax_iterate_succ_of_eq_of_ltproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Order.isMin_iterate_pred_of_eq_of_neproof · cited by 1
- toZ_iterate_succ_of_not_isMaxproof · cited by 1