Theorems · Theorem · order theory
Order.covBy_succ_of_not_isMax
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : SuccOrder α] {a : α}, ¬IsMax a → a ⋖ Order.succ a- Defined in
- Mathlib.Order.SuccPred.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 10 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 · cited by 633
- SuccOrderstatement and proof · cited by 574
- IsMaxstatement and proof · cited by 372
- CovBystatement · cited by 290
- Order.lt_succ_of_not_isMaxproof · cited by 25
- WCovBy.covBy_of_ltproof · cited by 6
- Order.wcovBy_succproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Order.IsSuccPrelimit.isMaxproof · cited by 7
- Order.covBy_succproof · cited by 6
- SuccOrder.nhdsGTproof · cited by 5
- OrderIso.map_succproof · cited by 4
- Order.not_isSuccPrelimit_iff_succ_eqproof · cited by 3
- SuccOrder.isOpen_singleton_of_not_isSuccPrelimitproof · cited by 1
- Order.pred_succ_of_not_isMaxproof · cited by 1
- SimpleGraph.hasse_preconnected_of_succproof · cited by 1