Theorems · Theorem · logic and foundations
Cardinal.ord_le
∀ {c : Cardinal.{u_1}} {o : Ordinal.{u_1}}, c.ord ≤ o ↔ c ≤ o.card- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.ordstatement · cited by 266
- Ordinal.cardstatement · cited by 122
- GaloisConnection.le_iff_leproof · cited by 17
- Cardinal.gc_ord_cardproof · cited by 6
Cited by10
Results whose statement or proof uses this declaration.
- Cardinal.isSuccLimit_ordproof · cited by 11
- Cardinal.ord_aleph0proof · cited by 9
- Cardinal.lift_ordproof · cited by 8
- Cardinal.ord_natCastproof · cited by 6
- Ordinal.exists_ord_cof_eqproof · cited by 5
- Ordinal.aleph0_le_cardproof · cited by 5
- Ordinal.nat_le_cardproof · cited by 4
- Ordinal.not_bddAbove_isInitialproof · cited by 3
- Order.ord_cof_eq_type_ltproof · cited by 2
- Order.type_eq_of_isCofinalproof · cited by 0