Theorems · Theorem · order theory
WithTop.iSup_coe_lt_top
∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompleteLinearOrderBot α] {f : ι → α},
⨆ x, ↑(f x) < ⊤ ↔ BddAbove (Set.range f)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 31 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.
- Top.topstatement · cited by 9,680
- Set.rangestatement · cited by 4,705
- WithTopstatement · cited by 3,754
- iSupstatement · cited by 2,415
- WithTop.somestatement · cited by 1,128
- BddAbovestatement · cited by 620
- lt_top_iff_ne_topproof · cited by 95
- ConditionallyCompleteLinearOrderBotstatement and proof · cited by 84
- Iff.not_leftproof · cited by 49
- WithTop.iSup_coe_eq_topproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- ENNReal.iSup_coe_lt_topproof · cited by 2
- ENat.iSup_natCast_lt_topproof · cited by 1