Theorems · Theorem · logic and foundations
Cardinal.le_ord_iff_card_le_of_lt_aleph0
∀ (o : Ordinal.{u_1}) {c : Cardinal.{u_1}}, c < Cardinal.aleph0 → (o ≤ c.ord ↔ o.card ≤ c)- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement and proof · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.ordstatement · cited by 266
- Ordinal.cardstatement · cited by 122
- Cardinal.lt_aleph0proof · cited by 19
- Cardinal.ord_natCastproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Ordinal.not_lt_enum_ord_mk_min_complproof · cited by 0