Theorems · Theorem · logic and foundations
Nat.card_prod
∀ (α : Type u_3) (β : Type u_4), Nat.card (α × β) = Nat.card α * Nat.card β
- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Cardinal.mkproof · cited by 942
- Nat.cardstatement · cited by 844
- Cardinal.liftproof · cited by 583
- Cardinal.toNatproof · cited by 153
- Cardinal.toNat_liftproof · cited by 41
- Cardinal.mk_prodproof · cited by 19
- Cardinal.toNat_mulproof · cited by 6
Cited by24
Results whose statement or proof uses this declaration.
- AddSubgroup.relIndex_mul_indexproof · cited by 12
- Subgroup.card_eq_card_quotient_mul_card_subgroupproof · cited by 8
- Field.finSepDegree_mul_finSepDegree_of_isAlgebraicproof · cited by 6
- Subgroup.IsComplement.card_mul_cardproof · cited by 4
- Subgroup.isComplement'_of_card_mul_and_disjointproof · cited by 2
- AddSubgroup.card_eq_card_quotient_mul_card_addSubgroupproof · cited by 2
- AddSubgroup.IsComplement.card_mul_cardproof · cited by 2
- coprime_card_of_isAddCyclic_prodproof · cited by 2
- Ideal.ncard_primesOver_mul_card_inertia_mul_finrankproof · cited by 1
- DihedralGroup.card_commute_oddproof · cited by 1
- RegularWreathProduct.cardproof · cited by 1
- Submodule.card_eq_card_quotient_mul_cardproof · cited by 1