Theorems · Theorem · logic and foundations
Cardinal.card_le_iff
∀ {o : Ordinal.{u_1}} {c : Cardinal.{u_1}}, o.card ≤ c ↔ o < (Order.succ c).ord- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 80 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
- Order.succstatement · cited by 633
- Cardinal.ordstatement · cited by 266
- Ordinal.cardstatement and proof · cited by 122
- Order.lt_succ_iffproof · cited by 22
- Cardinal.lt_ordproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- Cardinal.isRegular_succproof · cited by 6
- Ordinal.cof_eq_aleph0_of_isSuccLimitproof · cited by 1
- Ordinal.sInf_compl_lt_lift_ord_succproof · cited by 1
- Ordinal.mem_range_lift_of_card_leproof · cited by 0