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Theorems · Theorem · order theory

Order.pred_covBy

∀ {α : Type u_1} [inst : Preorder α] [inst_1 : PredOrder α] [NoMinOrder α] (a : α), Order.pred a ⋖ a
Defined in
Mathlib.Order.SuccPred.Basic
Cited by
4 results in Mathlib
Foundations
Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPredOrderNoMinOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Order.pred_eq_iff_covBy · cited by 2Order.pred_eq_iff_covByInitialSeg.map_pred · cited by 1InitialSeg.map_predOrder.succ_pred · cited by 0Order.succ_predOrder.sub_one_covBy · cited by 0Order.sub_one_covByPreorder · cited by 7952PreorderPredOrder · cited by 334PredOrderCovBy · cited by 290CovByOrder.pred · cited by 273Order.predNoMinOrder · cited by 247NoMinOrdernot_isMin · cited by 42not_isMinOrder.pred_covBy_of_not_isMin · cited by 8Order.pred_covBy_of_not_i…Order.pred_covByCITED BYCITES

Cites7

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

Cited by4

Results whose statement or proof uses this declaration.