Theorems · Theorem · group theory
alternatingGroup.nontrivial_of_three_le_card
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α], 3 ≤ Nat.card α → Nontrivial ↥(alternatingGroup α)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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 · cited by 1,375
- le_of_ltproof · cited by 1,175
- le_transproof · cited by 985
- Nat.cardstatement and proof · cited by 844
- lt_of_lt_of_leproof · cited by 438
- Nat.card_eq_fintype_cardproof · cited by 200
- alternatingGroupstatement · cited by 96
- Nat.Prime.posproof · cited by 83
- Nat.prime_twoproof · cited by 55
Cited by1
Results whose statement or proof uses this declaration.
- alternatingGroup.isMulCommutative_iff_card_le_threeproof · cited by 1