Theorems · Theorem · order theory
Order.IsSuccPrelimit.sSup_Iio
∀ {α : Type u_2} [inst : ConditionallyCompleteLinearOrderBot α] {x : α}, Order.IsSuccPrelimit x → sSup (Set.Iio x) = x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- Set.Iiostatement · cited by 1,166
- SupSet.sSupstatement and proof · cited by 954
- Order.IsSuccPrelimitstatement and proof · cited by 157
- ConditionallyCompleteLinearOrderBotstatement and proof · cited by 84
- csSup_emptyproof · cited by 28
- IsLUB.csSup_eqproof · cited by 19
- IsMin.Iio_eqproof · cited by 11
- eq_bot_or_bot_ltproof · cited by 4
- Order.IsSuccPrelimit.isLUB_Iioproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Ordinal.iSup_typein_limitproof · cited by 1
- sSup_Iio_eq_self_iff_isSuccPrelimitproof · cited by 1
- Order.IsSuccPrelimit.iSup_Iioproof · cited by 1
- Order.IsSuccLimit.sSup_Iioproof · cited by 0