Theorems · Theorem · order theory
OrderEmbedding.wellFoundedLT
∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] [WellFoundedLT β] (f : α ↪o β),
WellFoundedLT αA preorder which embeds into a well-founded preorder is itself well-founded.
- Defined in
- Mathlib.Order.Hom.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- OrderEmbeddingstatement and proof · cited by 619
- WellFoundedLTstatement and proof · cited by 491
- IsWellFounded.wfproof · cited by 43
- OrderEmbedding.wellFoundedproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- isNoetherian_iff_fg_wellFoundedproof · cited by 1
- Submodule.IsArtinian.of_isArtinian_tensorProduct_of_faithfullyFlatproof · cited by 1
- isArtinian_of_surjective_algebraMapproof · cited by 1