Theorems · Theorem · order theory
WellFounded.not_lt_min
∀ {α : Type u_1} {r : α → α → Prop} (H : WellFounded r) (s : Set α) {x : α} (hx : x ∈ s), ¬r x (H.min s ⋯)- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 20 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.
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
- WellFounded.minstatement and proof · cited by 33
- WellFounded.has_minproof · cited by 26
Cited by20
Results whose statement or proof uses this declaration.
- minpoly.minproof · cited by 15
- Set.IsWF.not_lt_minproof · cited by 7
- MvPowerSeries.coeff_eq_zero_of_lt_lexOrderproof · cited by 5
- Set.IsPWO.exists_le_minimalproof · cited by 3
- exists_covBy_of_wellFoundedLTproof · cited by 2
- exists_covBy_seq_of_wellFoundedLT_wellFoundedGTproof · cited by 2
- WellFounded.min_leproof · cited by 2
- Pi.Lex.wellFoundedproof · cited by 2
- Function.not_lt_argminOnproof · cited by 2
- WellFounded.min_eq_of_forall_not_ltproof · cited by 1
- WellFounded.notMem_of_lt_minproof · cited by 1