Theorems · Theorem · order theory
ciSup_of_not_bddAbove
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLinearOrder α] {f : ι → α},
¬BddAbove (Set.range f) → ⨆ i, f i = sSup ∅- Cited by
- 9 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
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.
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- iSupstatement · cited by 2,415
- SupSet.sSupstatement · cited by 954
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- csSup_of_not_bddAboveproof · cited by 16
Cited by9
Results whose statement or proof uses this declaration.
- MvPowerSeries.gaussNorm_nonnegproof · cited by 3
- Ordinal.iSup_add_oneproof · cited by 2
- Ordinal.lift_card_iSup_le_sum_cardproof · cited by 2
- cbiSup_eq_of_not_forallproof · cited by 2
- Dense.ciSup'proof · cited by 1
- OrderIso.map_ciSup'proof · cited by 1
- cbiSup_of_not_bddAboveproof · cited by 1
- ciSup_sup_leproof · cited by 1
- NNReal.natCast_iSupproof · cited by 0