Theorems · Theorem · logic and foundations
Cardinal.isPrimePow_iff
∀ {a : Cardinal.{u_1}}, IsPrimePow a ↔ Cardinal.aleph0 ≤ a ∨ ∃ n, a = ↑n ∧ IsPrimePow n- Defined in
- Mathlib.SetTheory.Cardinal.Divisibility
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Nat.cast_oneproof · cited by 2,501
- Nat.Primeproof · cited by 2,059
- LE.le.trans_ltproof · cited by 795
- Cardinal.aleph0statement and proof · cited by 521
- not_leproof · cited by 328
- Primeproof · cited by 277
- IsPrimePowstatement and proof · cited by 77
- Cardinal.natCast_lt_aleph0proof · cited by 47
- Prime.ne_zeroproof · cited by 47
- Cardinal.power_le_power_leftproof · cited by 9
- Cardinal.power_oneproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Field.nonempty_iffproof · cited by 0