Theorems · Theorem · order theory
WithTop.iSup_coe_eq_top
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLinearOrderBot α] {f : ι → α},
⨆ x, ↑(f x) = ⊤ ↔ ¬BddAbove (Set.range f)- Cited by
- 3 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.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Set.rangestatement and proof · cited by 4,705
- WithTopstatement and proof · cited by 3,754
- iSupstatement · cited by 2,415
- WithTop.somestatement and proof · cited by 1,128
- LT.lt.neproof · cited by 872
- BddAbovestatement and proof · cited by 620
- ConditionallyCompleteLinearOrderBotstatement and proof · cited by 84
- WithTop.coe_lt_coeproof · cited by 47
- WithTop.coe_lt_topproof · cited by 44
- WithTop.untopproof · cited by 36
- WithTop.coe_untopproof · cited by 17
Cited by3
Results whose statement or proof uses this declaration.
- ENat.iSup_natCast_eq_topproof · cited by 4
- WithTop.iSup_coe_lt_topproof · cited by 2
- ENNReal.iSup_coe_eq_topproof · cited by 1