Theorems · Theorem · logic and foundations
Cardinal.power_self_eq
∀ {c : Cardinal.{u_1}}, Cardinal.aleph0 ≤ c → c ^ c = 2 ^ c- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 6 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.
Cites11
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
- LT.lt.leproof · cited by 2,189
- le_reflproof · cited by 2,061
- Cardinal.aleph0statement and proof · cited by 521
- LE.le.antisymmproof · cited by 507
- Cardinal.natCast_le_aleph0proof · cited by 20
- Cardinal.mul_eq_selfproof · cited by 13
- Cardinal.cantorproof · cited by 12
- Cardinal.power_le_power_rightproof · cited by 6
- Cardinal.power_mulproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Cardinal.power_eq_two_powerproof · cited by 2
- Cardinal.mk_perm_eq_self_powerproof · cited by 2
- Cardinal.mk_equiv_of_lift_eqproof · cited by 1
- Cardinal.aleph0_power_aleph0proof · cited by 1
- Cardinal.prod_eq_two_powerproof · cited by 0
- Cardinal.mk_perm_eq_two_powerproof · cited by 0