Theorems · Theorem · logic and foundations
Cardinal.lt_ord
∀ {c : Cardinal.{u_1}} {o : Ordinal.{u_1}}, o < c.ord ↔ o.card < c- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 13 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.lt_iff_ltproof · cited by 6
- Cardinal.gc_ord_cardproof · cited by 6
Cited by13
Results whose statement or proof uses this declaration.
- Cardinal.mul_eq_selfproof · cited by 13
- Cardinal.ord_aleph0proof · cited by 9
- Cardinal.ord_univproof · cited by 8
- Cardinal.lift_ordproof · cited by 8
- Cardinal.card_le_iffproof · cited by 4
- Cardinal.IsInaccessible.preBeth_ordproof · cited by 3
- Ordinal.isPrincipal_add_ordproof · cited by 2
- Ordinal.isPrincipal_mul_ordproof · cited by 2
- Cardinal.card_typein_ltproof · cited by 2
- Cardinal.derivFamily_lt_ord_liftproof · cited by 2
- Cardinal.IsInaccessible.beth_ordproof · cited by 2
- Cardinal.lt_ord_succ_cardproof · cited by 0