Theorems · Theorem · order theory
IsWellFounded.induction
∀ {α : Type u} (r : α → α → Prop) [IsWellFounded α r] {motive : α → Prop} (a : α),
(∀ (x : α), (∀ (y : α), r y x → motive y) → motive x) → motive aInduction on a well-founded relation.
- Defined in
- Mathlib.Order.RelClasses
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- IsWellFounded
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsWellFounded.wfproof · cited by 43
- IsWellFoundedstatement and proof · cited by 18
Cited by5
Results whose statement or proof uses this declaration.
- WellFoundedLT.inductionproof · cited by 24
- IsNoetherian.inductionproof · cited by 2
- Profinite.NobelingProof.GoodProducts.span_iff_productsproof · cited by 2
- WellFoundedGT.inductionproof · cited by 1
- InitialSeg.eq_or_principalproof · cited by 0