Theorems · Theorem · order theory
Order.lt_succ_iff_not_isMax
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a : α}, a < Order.succ a ↔ ¬IsMax a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
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
- Order.succstatement and proof · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- Order.le_succproof · cited by 96
- LE.le.lt_of_not_geproof · cited by 21
- not_isMax_of_ltproof · cited by 6
- Order.max_of_succ_leproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Order.lt_succ_of_not_isMaxproof · cited by 25
- Order.lt_succ_iff_ne_topproof · cited by 1
- Order.Ioo_eq_empty_iff_le_succproof · cited by 0