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Theorems · Theorem · order theory

Order.le_pred_iff

∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] {a b : α} [NoMinOrder α], b ≤ Order.pred a ↔ b < a
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
3 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPredOrderNoMinOrder
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Around this declaration

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

Order.pred_lt_pred · cited by 2Order.pred_lt_predOrder.pred_lt_pred_iff · cited by 1Order.pred_lt_pred_iffOrder.pred_le_pred_iff · cited by 1Order.pred_le_pred_iffPreorder · cited by 7952PreorderPredOrder · cited by 334PredOrderOrder.pred · cited by 273Order.predNoMinOrder · cited by 247NoMinOrdernot_isMin · cited by 42not_isMinOrder.le_pred_iff_of_not_isMin · cited by 14Order.le_pred_iff_of_not_…Order.le_pred_iffCITED BYCITES

Cites6

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

Cited by3

Results whose statement or proof uses this declaration.