Theorems · Theorem · group theory
alternatingGroup.eq_bot_of_card_le_two
∀ {α : Type u_1} [inst : Fintype α] [inst_1 : DecidableEq α], Nat.card α ≤ 2 → 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.
Cites16
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
- Bot.botstatement and proof · cited by 4,720
- mul_oneproof · cited by 3,885
- Subgroupstatement · cited by 3,593
- Nontrivialproof · cited by 2,416
- Equiv.Permstatement and proof · cited by 1,375
- Nat.cardstatement and proof · cited by 844
- Nat.factorialproof · cited by 616
- LE.le.antisymmproof · cited by 507
- Nat.card_eq_fintype_cardproof · cited by 200
- alternatingGroupstatement and proof · cited by 96
- Fintype.one_lt_cardproof · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- IsMultiplyPretransitive.alternatingGroup_leproof · cited by 1