Theorems · Theorem · logic and foundations
IsWellFounded.mem_range_rank_of_le
∀ {α : Type u} {a : α} {r : α → α → Prop} [hwf : IsWellFounded α r] {o : Ordinal.{u}},
o ≤ IsWellFounded.rank r a → o ∈ Set.range (IsWellFounded.rank r)- Defined in
- Mathlib.SetTheory.Ordinal.Rank
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsWellFounded
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 · cited by 53,352
- Set.rangestatement · cited by 4,705
- Ordinalstatement and proof · cited by 1,688
- IsWellFoundedstatement and proof · cited by 18
- IsWellFounded.rankstatement and proof · cited by 9
- IsWellFounded.applyproof · cited by 5
- Acc.rankproof · cited by 4
- Acc.mem_range_rank_of_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsWellFounded.rank_eq_typeinproof · cited by 0