Theorems · Theorem · order theory
IsMax.succ_eq
∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : SuccOrder α] {a : α}, IsMax a → Order.succ a = aAlias of the reverse direction of Order.succ_eq_iff_isMax.
- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- PartialOrderSuccOrder
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.
- PartialOrderstatement and proof · cited by 6,410
- Order.succstatement · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement · cited by 372
- Order.succ_eq_iff_isMaxproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- Order.IsSuccPrelimit.succ_ltproof · cited by 7
- Order.le_succ_iff_eq_or_leproof · cited by 6
- OrderIso.map_succproof · cited by 4
- Order.IsSuccPrelimit.isMinproof · cited by 2
- Order.le_iff_eq_or_succ_leproof · cited by 1
- Monotone.biUnion_Ico_Ioc_map_succproof · cited by 0
- succ_notMem_iff_isMaxproof · cited by 0