Theorems · Theorem · logic and foundations
Ordinal.le_iSup
∀ {ι : Type u_3} (f : ι → Ordinal.{u}) [Small.{u, u_3} ι] (i : ι), f i ≤ ⨆ i, f ile_ciSup whenever the input type is small in the output universe. This lemma sometimes
fails to infer f in simple cases and needs it to be given explicitly.
- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Small
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- Smallstatement and proof · cited by 369
- le_ciSupproof · cited by 57
- Ordinal.bddAbove_of_smallproof · cited by 19
Cited by19
Results whose statement or proof uses this declaration.
- PSet.rank_lt_of_memproof · cited by 7
- Ordinal.iSup_iterate_eq_nfpproof · cited by 5
- Ordinal.nfpFamily_fpproof · cited by 4
- Ordinal.iSup_natCastproof · cited by 4
- Ordinal.lt_iSup_add_oneproof · cited by 3
- Ordinal.IsFundamentalSeq.iSup_add_one_eqproof · cited by 3
- Ordinal.lsub_le_succ_iSupproof · cited by 2
- Ordinal.foldr_le_nfpFamilyproof · cited by 2
- Ordinal.iterate_le_nfpproof · cited by 2
- Ordinal.succ_lt_iSup_of_ne_iSupproof · cited by 2
- Acc.rank_lt_of_relproof · cited by 1
- Ordinal.iSup_eq_lsub_iffproof · cited by 1