Theorems · Theorem · order theory
RelEmbedding.not_wellFounded
∀ {α : Type u_1} {r : α → α → Prop} [IsStrictOrder α r] (f : (fun x1 x2 => x1 > x2) ↪r r), ¬WellFounded r- Defined in
- Mathlib.Order.OrderIsoNat
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsStrictOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RelEmbeddingstatement and proof · cited by 281
- IsStrictOrderstatement and proof · cited by 28
- not_isEmpty_iffproof · cited by 19
- RelEmbedding.wellFounded_iff_isEmptyproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- not_strictAnti_of_wellFoundedLTproof · cited by 5
- IsArtinian.surjective_of_injective_endomorphismproof · cited by 4
- WellFoundedLT.finite_of_sSupIndepproof · cited by 2
- exists_covBy_seq_of_wellFoundedLT_wellFoundedGTproof · cited by 2
- wellQuasiOrderedLE_iffproof · cited by 1