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Theorems · Theorem · order theory

isMin_of_pred_notMem

∀ {α : Type u_3} [inst : PartialOrder α] {s : Set α} [s.OrdConnected] [inst_2 : PredOrder α] {a : ↑s},
  Order.pred ↑a ∉ s → IsMin a
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
1 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PartialOrderSet.OrdConnectedPredOrder
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Around this declaration

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

pred_notMem_iff_isMin · cited by 0pred_notMem_iff_isMinSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemPartialOrder · cited by 6410PartialOrderPredOrder · cited by 334PredOrderIsMin · cited by 277IsMinOrder.pred · cited by 273Order.predSet.OrdConnected · cited by 161Set.OrdConnectedOrder.pred_eq_iff_isMin · cited by 8Order.pred_eq_iff_isMinisMin_of_pred_notMemCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.