Theorems · Theorem · logic and foundations
Cardinal.add_eq_self
∀ {c : Cardinal.{u_1}}, Cardinal.aleph0 ≤ c → c + c = cIf α is an infinite type, then α ⊕ α and α have the same cardinality.
- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LE.le.transproof · cited by 3,151
- Cardinalstatement and proof · cited by 2,598
- le_antisymmproof · cited by 2,068
- Cardinal.aleph0statement and proof · cited by 521
- two_mulproof · cited by 232
- mul_le_mul_leftproof · cited by 31
- Cardinal.natCast_le_aleph0proof · cited by 20
- self_le_add_leftproof · cited by 18
- Cardinal.mul_eq_selfproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- Cardinal.add_eq_maxproof · cited by 13
- Cardinal.add_lt_of_ltproof · cited by 7
- Cardinal.add_le_of_leproof · cited by 1
- Cardinal.continuum_add_selfproof · cited by 0