Theorems · Theorem · order theory
Set.IsPWO.exists_le_minimal
∀ {α : Type u_2} [inst : Preorder α] {s : Set α} {a : α}, s.IsPWO → a ∈ s → ∃ b ≤ a, Minimal (fun x => x ∈ s) b- Defined in
- Mathlib.Order.WellFoundedSet
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Elemproof · cited by 7,166
- Set.ofPredproof · cited by 6,101
- LE.le.transproof · cited by 3,151
- Set.Nonemptyproof · cited by 2,627
- le_rflproof · cited by 1,558
- Minimalstatement · cited by 150
- Set.IsPWOstatement and proof · cited by 99
- WellFounded.minproof · cited by 33
- WellFounded.min_memproof · cited by 23
- WellFounded.not_lt_minproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- Set.IsPWO.exists_minimalproof · cited by 1
- SemigroupIdeal.fg_of_wellQuasiOrderedLEproof · cited by 0
- AddSemigroupIdeal.fg_of_wellQuasiOrderedLEproof · cited by 0