Theorems · Definition · order theory
transfiniteIterate
{I : Type u} →
[SupSet I] → (I → I) → {J : Type w} → [inst : LinearOrder J] → [SuccOrder J] → [WellFoundedLT J] → J → I → IThe jth-iteration of a function φ : I → I when j : J belongs to
a well-ordered type.
- Defined in
- Mathlib.Order.TransfiniteIteration
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Set.Elemproof · cited by 7,166
- iSupproof · cited by 2,415
- Set.Iioproof · cited by 1,166
- SuccOrderstatement and proof · cited by 574
- WellFoundedLTstatement and proof · cited by 491
- IsMaxproof · cited by 372
- IsMinproof · cited by 277
- Order.IsSuccLimitproof · cited by 255
- SupSetstatement and proof · cited by 154
- SuccOrder.limitRecOnproof · cited by 14
Cited by17
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.strictLimitsClosureIterproof · cited by 5
- transfiniteIterate_succstatement · cited by 4
- transfiniteIterate_limitstatement · cited by 3
- monotone_transfiniteIteratestatement and proof · cited by 3
- transfiniteIterate_botstatement · cited by 2
- top_mem_range_transfiniteIteratestatement and proof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.exists_ordinalstatement · cited by 1
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.top_mem_rangestatement and proof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.generatingMonomorphisms.transfiniteCompositionOfShapeOfEqTopstatement and proof · cited by 1
- CategoryTheory.ObjectProperty.strictLimitsClosureIter_le_limitsClosureproof · cited by 1