Theorems · Theorem · logic and foundations
Cardinal.power_lt_aleph0
∀ {a b : Cardinal.{u_1}}, a < Cardinal.aleph0 → b < Cardinal.aleph0 → a ^ b < Cardinal.aleph0- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Cardinal.aleph0statement and proof · cited by 521
- Nat.cast_powproof · cited by 131
- Cardinal.natCast_lt_aleph0proof · cited by 47
- Cardinal.lt_aleph0proof · cited by 19
- Cardinal.power_natCastproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- max_aleph0_card_le_rank_fun_natproof · cited by 1
- Cardinal.power_nat_le_maxproof · cited by 1
- cardinal_lt_aleph0_of_finiteDimensionalproof · cited by 0
- Cardinal.powerlt_aleph0_leproof · cited by 0