Theorems · Definition · order theory
WellFounded.min
{α : Type u_1} → {r : α → α → Prop} → WellFounded r → (s : Set α) → s.Nonempty → αA minimal element of a nonempty set in a well-founded order.
If you're working with a nonempty linear order, consider defining a
ConditionallyCompleteLinearOrderBot instance via
WellFoundedLT.conditionallyCompleteLinearOrderBot and using Inf instead.
- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 33 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.
Cites3
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.has_minproof · cited by 26
Cited by44
Results whose statement or proof uses this declaration.
- minpolyproof · cited by 439
- Set.IsWF.minproof · cited by 47
- WellFounded.min_memstatement and proof · cited by 23
- Set.IsWF.min_memproof · cited by 20
- WellFounded.not_lt_minstatement and proof · cited by 20
- MvPowerSeries.lexOrderproof · cited by 14
- Field.Emb.Cardinal.leastExtproof · cited by 13
- Function.argminOnproof · cited by 8
- minpoly.algHom_eqproof · cited by 8
- RatFunc.uniformizingPolynomialproof · cited by 7
- MvPowerSeries.coeff_eq_zero_of_lt_lexOrderproof · cited by 5
- Function.argminproof · cited by 4