Theorems · Theorem · logic and foundations
Cardinal.aleph0_add_nat
∀ (n : ℕ), Cardinal.aleph0 + ↑n = Cardinal.aleph0
- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 2 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Cardinalstatement · cited by 2,598
- le_rflproof · cited by 1,558
- Cardinal.aleph0statement · cited by 521
- LE.le.antisymmproof · cited by 507
- le_self_addproof · cited by 68
- Cardinal.natCast_le_aleph0proof · cited by 20
- Cardinal.add_le_aleph0proof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Cardinal.nat_add_aleph0proof · cited by 1
- Cardinal.aleph0_add_ofNatproof · cited by 0