Theorems · Definition · order theory
Set.IsWF.min
{α : Type u_2} → [inst : Preorder α] → {s : Set α} → s.IsWF → s.Nonempty → αSet.IsWF.min returns a minimal element of a nonempty well-founded set.
- Defined in
- Mathlib.Order.WellFoundedSet
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 15 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.
Cites6
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.univproof · cited by 3,945
- Set.Nonemptystatement and proof · cited by 2,627
- Set.IsWFstatement and proof · cited by 47
- WellFounded.minproof · cited by 33
Cited by49
Results whose statement or proof uses this declaration.
- HahnSeries.orderTopproof · cited by 103
- HahnSeries.orderproof · cited by 52
- Set.IsWF.min_memstatement · cited by 20
- HahnSeries.orderTop_of_ne_zerostatement · cited by 17
- Set.IsWF.min_lestatement · cited by 14
- HahnSeries.order_of_nestatement · cited by 13
- HahnSeries.leadingCoeff_of_ne_zeroproof · cited by 11
- Set.IsWF.min_le_min_of_subsetstatement · cited by 7
- Set.IsWF.not_lt_minstatement · cited by 7
- HahnSeries.orderTop_negproof · cited by 6
- HahnSeries.orderTop_singleproof · cited by 6
- Set.IsWF.le_min_iffstatement and proof · cited by 5