Theorems · Theorem · logic and foundations
Cardinal.ord_lt_ord
∀ {c₁ c₂ : Cardinal.{u_1}}, c₁.ord < c₂.ord ↔ c₁ < c₂- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 1,688
- Cardinal.ordstatement · cited by 266
- StrictMono.lt_iff_ltproof · cited by 86
- Cardinal.ord_strictMonoproof · cited by 7
Cited by7
Results whose statement or proof uses this declaration.
- Cardinal.lift_iSup_lt_of_lt_cof_ordproof · cited by 4
- Cardinal.iSup_lt_of_lt_cof_ordproof · cited by 4
- Cardinal.lt_univproof · cited by 1
- Ordinal.ord_mk_lt_typeproof · cited by 1
- Cardinal.sSup_lt_of_lt_cof_ordproof · cited by 0
- Ordinal.IsFundamentalSeq.iSup_eqproof · cited by 0
- Cardinal.ord_posproof · cited by 0