Theorems · Theorem · group theory
two_mul_nat_card_alternatingGroup
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α] [Nontrivial α],
2 * Nat.card ↥(alternatingGroup α) = Nat.card (Equiv.Perm α)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqNontrivial
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.
- Fintypestatement and proof · cited by 7,736
- Subgroupstatement · cited by 3,593
- Nontrivialstatement and proof · cited by 2,416
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- alternatingGroupstatement and proof · cited by 96
- Subgroup.index_mul_cardproof · cited by 7
- alternatingGroup.index_eq_twoproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- alternatingGroup.eq_bot_of_card_le_twoproof · cited by 1
- two_mul_card_alternatingGroupproof · cited by 1
- alternatingGroup.nontrivial_of_three_le_cardproof · cited by 1