Theorems · Theorem · logic and foundations
Cardinal.add_one_of_aleph0_le
∀ {c : Cardinal.{u_1}}, Cardinal.aleph0 ≤ c → c + 1 = c- Defined in
- Mathlib.SetTheory.Ordinal.Arithmetic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Ordinalproof · cited by 1,688
- add_commproof · cited by 1,535
- Cardinal.aleph0statement and proof · cited by 521
- Cardinal.ordproof · cited by 266
- Ordinal.cardproof · cited by 122
- Cardinal.card_ordproof · cited by 23
- Cardinal.ord_aleph0proof · cited by 9
- Cardinal.ord_le_ordproof · cited by 7
- Ordinal.card_addproof · cited by 6
- Ordinal.card_oneproof · cited by 6
- Ordinal.one_add_of_omega0_leproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Cardinal.isSuccLimit_ordproof · cited by 11
- Cardinal.add_one_eqproof · cited by 2
- Ordinal.isInitial_succproof · cited by 0