Theorems · Theorem · order theory
not_acc_iff_exists_descending_chain
∀ {α : Sort u_1} {r : α → α → Prop} {x : α}, ¬Acc r x ↔ ∃ f, f 0 = x ∧ ∀ (n : ℕ), r (f (n + 1)) (f n)- Defined in
- Mathlib.Order.WellFounded
- Cited by
- 2 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.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- exists_not_acc_lt_of_not_accproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- RelEmbedding.acc_iff_isEmpty_subtype_mem_rangeproof · cited by 2
- acc_iff_isEmpty_descending_chainproof · cited by 1