Theorems · Theorem · group theory
AddSubgroup.eq_bot_or_eq_top_of_prime_card
∀ {G : Type u_2} [inst : AddGroup G] (H : AddSubgroup G) [hp : Fact (Nat.Prime (Nat.card G))], H = ⊥ ∨ H = ⊤- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- Bot.botstatement and proof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Finiteproof · cited by 3,029
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Nat.cardstatement and proof · cited by 844
- Fact.outproof · cited by 328
- Nat.Prime.ne_zeroproof · cited by 109
- Nat.finite_of_card_ne_zeroproof · cited by 33
- Nat.dvd_primeproof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- zmultiples_eq_top_of_prime_cardproof · cited by 1
- isSimpleAddGroup_of_prime_cardproof · cited by 1