Theorems · Theorem · order theory
exists_eq_ciSup_of_not_isSuccLimit
∀ {ι : Sort u_1} {α : Type u_2} [inst : ConditionallyCompleteLinearOrder α] [Nonempty ι] {f : ι → α},
BddAbove (Set.range f) → ¬Order.IsSuccLimit (⨆ i, f i) → ∃ i, f i = ⨆ i, f i- Cited by
- 5 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement and proof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- Order.IsSuccLimitstatement and proof · cited by 255
- Set.range_nonemptyproof · cited by 84
- csSup_mem_of_not_isSuccLimitproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- exists_finset_linearIndependent_of_le_rankproof · cited by 3
- Cardinal.ciSup_addproof · cited by 2
- Cardinal.ciSup_mulproof · cited by 2
- Cardinal.exists_eq_natCast_of_iSup_eqproof · cited by 0
- Cardinal.exists_eq_of_iSup_eq_of_not_isSuccLimitproof · cited by 0