Theorems · Theorem · order theory
ENat.exists_eq_iSup_of_lt_top
∀ {ι : Sort u_1} {f : ι → ℕ∞} [Nonempty ι], ⨆ i, f i < ⊤ → ∃ i, f i = ⨆ i, f i- Defined in
- Mathlib.Data.ENat.Lattice
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Nonempty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- ENatstatement and proof · cited by 4,985
- iSupstatement and proof · cited by 2,415
- ENat.sSup_mem_of_nonempty_of_lt_topproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- ENat.mul_iSupproof · cited by 3
- ENat.exists_eq_iSup₂_of_lt_topproof · cited by 1
- Set.exists_eq_chainHeight_of_chainHeight_ne_topproof · cited by 1
- Metric.exists_set_encard_eq_packingNumberproof · cited by 0
- SimpleGraph.exists_eccent_eq_ediam_of_ne_topproof · cited by 0