Theorems · Theorem · logic and foundations
Nat.card_congr
∀ {α : Type u_1} {β : Type u_2} (f : α ≃ β), Nat.card α = Nat.card β- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 133 results in Mathlib
- Foundations
- Depth 93 from the axioms, rests on 2,432 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivstatement and proof · cited by 8,337
- Nat.cardstatement · cited by 844
- Cardinal.toNat_congrproof · cited by 2
Cited by133
Results whose statement or proof uses this declaration.
- IsGalois.card_aut_eq_finrankproof · cited by 16
- Subgroup.relIndex_mul_indexproof · cited by 14
- Nat.card_zpowersproof · cited by 13
- AddSubgroup.relIndex_mul_indexproof · cited by 12
- Nat.card_zmultiplesproof · cited by 11
- Subgroup.card_eq_card_quotient_mul_card_subgroupproof · cited by 8
- Field.finSepDegree_mul_finSepDegree_of_isAlgebraicproof · cited by 6
- Nat.card_unitsproof · cited by 6
- Subgroup.index_comap_of_surjectiveproof · cited by 5
- NumberField.absNorm_differentIdealproof · cited by 4
- MulAction.index_stabilizerproof · cited by 4
- Subgroup.IsComplement.card_mul_cardproof · cited by 4