Theorems · Theorem · logic and foundations
Cardinal.prod_eq_two_power
∀ {ι : Type u} [Infinite ι] {c : ι → Cardinal.{v}},
(∀ (i : ι), 2 ≤ c i) →
(∀ (i : ι), Cardinal.lift.{u, v} (c i) ≤ Cardinal.lift.{v, u} (Cardinal.mk ι)) →
Cardinal.prod c = 2 ^ Cardinal.lift.{v, u} (Cardinal.mk ι)- Defined in
- Mathlib.SetTheory.Cardinal.Arithmetic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Infinite
Around this declaration
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Cites20
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
- le_antisymmproof · cited by 2,068
- Cardinal.mkstatement and proof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Infinitestatement and proof · cited by 352
- LE.le.trans_eqproof · cited by 328
- Cardinal.lift_leproof · cited by 78
- Cardinal.lift_umaxproof · cited by 56
- Cardinal.lift_liftproof · cited by 53
- Cardinal.lift_id'proof · cited by 43
- Cardinal.aleph0_le_mkproof · cited by 32
- Cardinal.prodstatement and proof · cited by 16
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