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Theorems · Theorem · order theory

isMax_of_succ_notMem

∀ {α : Type u_3} [inst : PartialOrder α] {s : Set α} [s.OrdConnected] [inst_2 : SuccOrder α] {a : ↑s},
  Order.succ ↑a ∉ s → IsMax a
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
1 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderSet.OrdConnectedSuccOrder
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

succ_notMem_iff_isMax · cited by 0succ_notMem_iff_isMaxDFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemPartialOrder · cited by 6410PartialOrderSet.preimage · cited by 4946Set.preimageOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderOrderDual.ofDual · cited by 400OrderDual.ofDualIsMax · cited by 372IsMaxOrder.pred · cited by 273Order.predSet.OrdConnected · cited by 161Set.OrdConnectedOrder.succ_eq_iff_isMax · cited by 11Order.succ_eq_iff_isMaxisMax_of_succ_notMemCITED BYCITES

Cites12

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Cited by1

Results whose statement or proof uses this declaration.