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Theorems · Theorem · order theory

Set.IsPWO.exists_minimal

∀ {α : Type u_2} [inst : Preorder α] {s : Set α}, s.IsPWO → s.Nonempty → ∃ a, Minimal (fun x => x ∈ s) a
Defined in
Mathlib.Order.WellFoundedSet
Cited by
1 results in Mathlib
Foundations
Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Preorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.IsPWO.exists_minimalFor · cited by 0IsPWO.exists_minimalForSet · cited by 53352SetPreorder · cited by 7952PreorderSet.Nonempty · cited by 2627Set.NonemptyMinimal · cited by 150MinimalSet.IsPWO · cited by 99Set.IsPWOSet.IsPWO.exists_le_minimal · cited by 3IsPWO.exists_le_minimalIsPWO.exists_minimalCITED BYCITES

Cites6

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.