Theorems · Theorem · logic and foundations
Cardinal.prod_eq_of_fintype
∀ {α : Type u} [h : Fintype α] (f : α → Cardinal.{v}), Cardinal.prod f = Cardinal.lift.{u, v} (∏ i, f i)- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Fintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- Equivproof · cited by 8,337
- Fintypestatement and proof · cited by 7,736
- Equiv.symmproof · cited by 3,681
- Finset.univstatement and proof · cited by 3,473
- Cardinalstatement and proof · cited by 2,598
- Finset.prodstatement and proof · cited by 2,356
- Cardinal.mkproof · cited by 942
- Cardinal.liftstatement and proof · cited by 583
- Cardinal.lift_idproof · cited by 163
- Quotient.outproof · cited by 141
Cited by2
Results whose statement or proof uses this declaration.
- Nat.card_piproof · cited by 10
- Set.encard_pi_eq_prod_encardproof · cited by 0