Theorems · Theorem · order theory
transfiniteIterate_limit
∀ {I : Type u} [inst : SupSet I] (φ : I → I) {J : Type w} [inst_1 : LinearOrder J] [inst_2 : SuccOrder J]
[inst_3 : WellFoundedLT J] (i₀ : I) (j : J),
Order.IsSuccLimit j → transfiniteIterate φ j i₀ = ⨆ x, transfiniteIterate φ (↑x) i₀- Defined in
- Mathlib.Order.TransfiniteIteration
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.Elemstatement and proof · cited by 7,166
- iSupstatement and proof · cited by 2,415
- Set.Iiostatement and proof · 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.IsSuccLimitstatement and proof · cited by 255
- SupSetstatement and proof · cited by 154
- iSup_applyproof · cited by 35
Cited by3
Results whose statement or proof uses this declaration.
- monotone_transfiniteIterateproof · cited by 3
- CategoryTheory.ObjectProperty.strictLimitsClosureIter_le_limitsClosureproof · cited by 1