Theorems · Theorem · order theory
Order.lt_succ_of_not_isMax
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a : α}, ¬IsMax a → a < Order.succ aAlias of the reverse direction of Order.lt_succ_iff_not_isMax.
- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 9 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
- Order.lt_succ_iff_not_isMaxproof · cited by 3
Cited by30
Results whose statement or proof uses this declaration.
- Order.lt_succproof · cited by 45
- Order.succ_le_iff_of_not_isMaxproof · cited by 15
- Order.covBy_succ_of_not_isMaxproof · cited by 8
- Order.lt_succ_of_le_of_not_isMaxproof · cited by 4
- Order.IsNormal.of_succ_ltproof · cited by 4
- StrictMonoOn.Iic_id_leproof · cited by 3
- InverseSystem.PEquivOn.extproof · cited by 2
- InverseSystem.PEquivOn.casesOnstatement and proof · cited by 1
- InverseSystem.PEquivOn.compatstatement · cited by 1
- InverseSystem.PEquivOn.mk.noConfusionstatement and proof · cited by 1
- Order.Icc_subset_Ico_succ_right_of_not_isMaxproof · cited by 1
- iSup_succproof · cited by 1