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Theorems · Theorem · order theory

Order.pred_succ_of_not_isMax

∀ {α : Type u_1} [inst : PartialOrder α] [inst_1 : PredOrder α] [inst_2 : SuccOrder α] {a : α},
  ¬IsMax a → Order.pred (Order.succ a) = 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
PartialOrderPredOrderSuccOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.pred_succ_iterate_of_not_isMax · cited by 0Order.pred_succ_iterate_o…PartialOrder · cited by 6410PartialOrderOrder.succ · cited by 633Order.succSuccOrder · cited by 574SuccOrderIsMax · cited by 372IsMaxPredOrder · cited by 334PredOrderOrder.pred · cited by 273Order.predOrder.covBy_succ_of_not_isMax · cited by 8Order.covBy_succ_of_not_i…CovBy.pred_eq · cited by 8CovBy.pred_eqOrder.pred_succ_of_not_isMaxCITED BYCITES

Cites8

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Cited by1

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