Theorems · Theorem · order theory
Set.IsWF.not_lt_min
∀ {α : Type u_2} [inst : Preorder α] {s : Set α} {a : α} (hs : s.IsWF) (hn : s.Nonempty), a ∈ s → ¬a < hs.min hn- Defined in
- Mathlib.Order.WellFoundedSet
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 16 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.
Cites8
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.mem_univproof · cited by 416
- Set.IsWFstatement and proof · cited by 47
- Set.IsWF.minstatement · cited by 47
- WellFounded.not_lt_minproof · cited by 20
Cited by7
Results whose statement or proof uses this declaration.
- Set.IsWF.min_leproof · cited by 14
- HahnSeries.coeff_eq_zero_of_lt_orderTopproof · cited by 9
- HahnSeries.coeff_eq_zero_of_lt_orderproof · cited by 3
- Set.IsWF.min_of_subset_not_lt_minproof · cited by 2
- LaurentSeries.Cauchy.exists_lb_eventual_supportproof · cited by 2
- Set.IsWF.min_eq_of_leproof · cited by 1
- Set.IsWF.min_eq_of_ltproof · cited by 0