Theorems · Theorem · order theory
WellFounded.wellFounded_iff_has_min
∀ {α : Type u_1} {r : α → α → Prop}, WellFounded r ↔ ∀ (s : Set α), s.Nonempty → ∃ m ∈ s, ∀ x ∈ s, ¬r x m- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- Set.ofPredproof · cited by 6,101
- Set.Nonemptystatement and proof · cited by 2,627
- WellFounded.has_minproof · cited by 26
Cited by5
Results whose statement or proof uses this declaration.
- set_has_maximal_iff_noetherianproof · cited by 3
- Set.wellFoundedOn_iffproof · cited by 1
- set_has_minimal_iff_artinianproof · cited by 1
- WellFounded.wellFoundedGT_iff_exists_maximalproof · cited by 1