Theorems · Theorem · combinatorics
Fintype.card_prod
∀ (α : Type u_4) (β : Type u_5) [inst : Fintype α] [inst_1 : Fintype β], Fintype.card (α × β) = Fintype.card α * Fintype.card β
- Defined in
- Mathlib.Data.Fintype.Prod
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Finset.univproof · cited by 3,473
- Fintype.cardstatement · cited by 1,386
- Finset.card_productproof · cited by 39
Cited by19
Results whose statement or proof uses this declaration.
- orderOf_dvd_cardproof · cited by 9
- addOrderOf_dvd_cardproof · cited by 5
- Nat.totient_mulproof · cited by 5
- MulAction.card_orbit_mul_card_stabilizer_eq_card_groupproof · cited by 4
- Module.Invertible.free_iff_linearEquivproof · cited by 3
- Projectivization.cardproof · cited by 3
- corners_theoremproof · cited by 2
- MulAction.sum_card_fixedBy_eq_card_orbits_mul_card_groupproof · cited by 1
- commProb_eq_one_iffproof · cited by 1
- Equiv.Perm.OnCycleFactors.kerParam_range_cardproof · cited by 1
- AddAction.card_eq_sum_card_addGroup_sub_card_stabilizer'proof · cited by 1
- Numbering.card_prefixedproof · cited by 1