Theorems · Theorem · logic and foundations
Ordinal.card_sSup_le
∀ {c : Cardinal.{u}} {s : Set Ordinal.{u}},
Cardinal.mk ↑s ≤ Cardinal.lift.{u + 1, u} c → (∀ x ∈ s, x.card ≤ c) → (sSup s).card ≤ c- Defined in
- Mathlib.SetTheory.Cardinal.Ordinal
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Cardinalstatement and proof · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- SupSet.sSupstatement · cited by 954
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Ordinal.cardstatement and proof · cited by 122
- Cardinal.lift_id'proof · cited by 43
- sSup_eq_iSup'proof · cited by 38
- Ordinal.card_iSup_le_liftproof · cited by 3
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