Theorems · Theorem · order theory
Order.IsNormal.apply_of_isSuccLimit
∀ {α : Type u_1} {β : Type u_2} {a : α} {f : α → β} [inst : ConditionallyCompleteLinearOrderBot α]
[inst_1 : ConditionallyCompleteLinearOrder β], Order.IsNormal f → Order.IsSuccLimit a → f a = ⨆ b, f ↑b- Defined in
- Mathlib.Order.IsNormal
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Set.rangeproof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- LT.lt.leproof · cited by 2,189
- Set.Iiostatement and proof · cited by 1,166
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- Order.IsSuccLimitstatement and proof · cited by 255
- Order.IsNormalstatement and proof · cited by 118
- ConditionallyCompleteLinearOrderBotstatement and proof · cited by 84
- Order.IsNormal.map_iSupproof · cited by 8
- Order.IsSuccLimit.iSup_Iioproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- Ordinal.cof_map_of_isNormalproof · cited by 7
- Ordinal.op_eq_self_of_isPrincipalproof · cited by 3
- Ordinal.card_opow_le_of_omega0_le_leftproof · cited by 3
- Ordinal.mul_eq_opow_log_succproof · cited by 0
- Cardinal.aleph_limitproof · cited by 0
- Cardinal.beth_limitproof · cited by 0
- Cardinal.preAleph_limitproof · cited by 0