Theorems · Theorem · logic and foundations
Ordinal.lift_iSup_lt_of_lt_cof
∀ {β : Type v} {f : β → Ordinal.{u}} {a : Ordinal.{u}},
Cardinal.lift.{u, v} (Cardinal.mk β) < (Ordinal.lift.{v, u} a).cof → (∀ (i : β), f i < a) → ⨆ i, f i < a- Cited by
- 8 results in Mathlib
- Foundations
- Depth 90 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.
- Cardinalstatement · cited by 2,598
- iSupstatement · cited by 2,415
- Ordinalstatement and proof · cited by 1,688
- Cardinal.mkstatement and proof · cited by 942
- LE.le.trans_ltproof · cited by 795
- Cardinal.liftstatement and proof · cited by 583
- Ordinal.cofstatement and proof · cited by 125
- Ordinal.liftstatement and proof · cited by 86
- Ordinal.lift_iSup_add_one_lt_of_lt_cofproof · cited by 6
- Ordinal.iSup_le_iSup_add_oneproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- Ordinal.iSup_lt_of_lt_cofproof · cited by 5
- Cardinal.lift_iSup_lt_of_lt_cof_ordproof · cited by 4
- Ordinal.nfpFamily_lt_ord_liftproof · cited by 4
- Cardinal.derivFamily_lt_ord_liftproof · cited by 2
- Ordinal.iSup_lt_omega_oneproof · cited by 1
- Ordinal.cof_iSup_le_liftproof · cited by 0
- Ordinal.iSup_lt_ord_liftproof · cited by 0
- Cardinal.iSup_lt_ord_lift_of_isRegularproof · cited by 0