Theorems · Theorem · logic and foundations
Ordinal.iSup_le_iff
∀ {ι : Type u_3} {f : ι → Ordinal.{u}} {a : Ordinal.{u}} [Small.{u, u_3} ι], ⨆ i, f i ≤ a ↔ ∀ (i : ι), f i ≤ aciSup_le_iff' whenever the input type is small in the output universe.
- Defined in
- Mathlib.SetTheory.Ordinal.Family
- Cited by
- 9 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
- Ordinal.bddAbove_of_smallproof · cited by 19
- ciSup_le_iff'proof · cited by 10
Cited by9
Results whose statement or proof uses this declaration.
- Ordinal.opow_le_of_isSuccLimitproof · cited by 7
- Ordinal.iSup_iterate_eq_nfpproof · cited by 5
- Ordinal.bsup_le_iffproof · cited by 4
- Ordinal.derivFamily_fpproof · cited by 3
- Ordinal.op_eq_self_of_isPrincipalproof · cited by 3
- Ordinal.nfp_le_iffproof · cited by 2
- Ordinal.le_iff_derivFamilyproof · cited by 2
- Ordinal.mul_eq_opow_log_succproof · cited by 0
- Ordinal.nfpFamily_le_iffproof · cited by 0