Theorems · Theorem · order theory
WellFounded.min_mem
∀ {α : Type u_1} {r : α → α → Prop} (H : WellFounded r) (s : Set α) (h : s.Nonempty), H.min s h ∈ s- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 15 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.Nonemptystatement and proof · cited by 2,627
- WellFounded.minstatement and proof · cited by 33
- WellFounded.has_minproof · cited by 26
Cited by23
Results whose statement or proof uses this declaration.
- minpoly.aevalproof · cited by 91
- minpoly.monicproof · cited by 81
- Function.argminOn_memproof · cited by 7
- Field.Emb.Cardinal.isLeast_leastExtproof · cited by 4
- Set.IsPWO.exists_le_minimalproof · cited by 3
- RatFunc.uniformizingPolynomial_ne_zeroproof · cited by 2
- exists_covBy_of_wellFoundedLTproof · cited by 2
- exists_covBy_seq_of_wellFoundedLT_wellFoundedGTproof · cited by 2
- IsUpperSet.eq_empty_or_Iciproof · cited by 2
- MvPowerSeries.coeff_ne_zero_of_lexOrderproof · cited by 2
- IsLowerSet.eq_empty_or_Iicproof · cited by 2