Theorems · Theorem · order theory
transfiniteIterate_bot
∀ {I : Type u} [inst : SupSet I] (φ : I → I) {J : Type w} [inst_1 : LinearOrder J] [inst_2 : SuccOrder J]
[inst_3 : WellFoundedLT J] [inst_4 : OrderBot J] (i₀ : I), transfiniteIterate φ ⊥ i₀ = i₀- Defined in
- Mathlib.Order.TransfiniteIteration
- Cited by
- 2 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.
Cites14
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
- Bot.botstatement and proof · cited by 4,720
- iSupproof · cited by 2,415
- Set.Iioproof · cited by 1,166
- OrderBotstatement and proof · cited by 1,055
- 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
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.ObjectProperty.le_strictLimitsClosureIterproof · cited by 1
- CategoryTheory.ObjectProperty.strictLimitsClosureIter_le_limitsClosureproof · cited by 1