Theorems · Theorem · logic and foundations
Nat.card_sum
∀ {α : Type u_1} {β : Type u_2} [Finite α] [Finite β], Nat.card (α ⊕ β) = Nat.card α + Nat.card β- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Fintype.cardproof · cited by 1,386
- Nat.cardstatement · cited by 844
- Fintype.ofFiniteproof · cited by 255
- Nat.card_eq_fintype_cardproof · cited by 200
- Fintype.card_sumproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Nat.card_unitsproof · cited by 6
- Ideal.card_norm_le_eq_card_norm_le_add_oneproof · cited by 2
- DihedralGroup.card_commute_oddproof · cited by 1
- CategoryTheory.PreGaloisCategory.card_fiber_coprod_eq_sumproof · cited by 0