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Theorems · Theorem · order theory

coe_pred_of_mem

∀ {α : Type u_3} [inst : PartialOrder α] {s : Set α} [inst_1 : s.OrdConnected] [inst_2 : PredOrder α] {a : ↑s},
  Order.pred ↑a ∈ s → ↑(Order.pred a) = Order.pred ↑a
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
2 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.

Set.Ici.coe_pred_of_not_isMin · cited by 1Ici.coe_pred_of_not_isMinpred_notMem_iff_isMin · cited by 0pred_notMem_iff_isMinSet · cited by 53352SetSet.Elem · cited by 7166Set.ElemPartialOrder · cited by 6410PartialOrderPredOrder · cited by 334PredOrderOrder.pred · cited by 273Order.predSet.OrdConnected · cited by 161Set.OrdConnectedcoe_pred_of_memCITED BYCITES

Cites6

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Cited by2

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