Theorems · Theorem · order theory
acc_iff_isEmpty_descending_chain
∀ {α : Sort u_1} {r : α → α → Prop} {x : α}, Acc r x ↔ IsEmpty { f // f 0 = x ∧ ∀ (n : ℕ), r (f (n + 1)) (f n) }- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 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.
- IsEmptystatement · cited by 759
- nonempty_subtypeproof · cited by 22
- not_acc_iff_exists_descending_chainproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- wellFounded_iff_isEmpty_descending_chainproof · cited by 5