Theorems · Theorem · order theory
Order.succ_eq_iff_isMax
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : SuccOrder α] {a : α}, Order.succ a = a ↔ IsMax a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PartialOrderSuccOrder
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.
- PartialOrderstatement and proof · cited by 6,410
- Order.succstatement and proof · cited by 633
- Eq.leproof · cited by 605
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- Order.le_succproof · cited by 96
- IsMax.eq_of_geproof · cited by 7
- Order.max_of_succ_leproof · cited by 6
Cited by11
Results whose statement or proof uses this declaration.
- IsMax.succ_eqproof · cited by 7
- strictMonoOn_of_lt_succproof · cited by 4
- monotoneOn_of_le_succproof · cited by 3
- StrictMonoOn.Iic_id_leproof · cited by 3
- Order.succ_topproof · cited by 1
- sup_Ioc_disjointed_of_monotoneproof · cited by 1
- Monotone.disjointed_succ_supproof · cited by 1
- WithTop.succ_coe_of_not_isMaxproof · cited by 1
- isMax_of_succ_notMemproof · cited by 1
- Order.not_isMin_succproof · cited by 1
- WithTop.succ_coe_of_isMaxproof · cited by 0