Theorems · Theorem · logic and foundations
Ordinal.card_add
∀ (o₁ o₂ : Ordinal.{u_1}), (o₁ + o₂).card = o₁.card + o₂.card- Defined in
- Mathlib.SetTheory.Ordinal.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 32 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 · cited by 2,598
- Ordinalstatement and proof · cited by 1,688
- IsWellOrderproof · cited by 171
- Ordinal.cardstatement · cited by 122
- Ordinal.inductionOn₂proof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Ordinal.card_natproof · cited by 6
- Cardinal.add_one_of_aleph0_leproof · cited by 3
- Ordinal.isPrincipal_add_ordproof · cited by 2
- Ordinal.card_add_oneproof · cited by 2
- Ordinal.card_succproof · cited by 0
- Ordinal.isInitial_succproof · cited by 0