Theorems · Theorem · group theory
Subgroup.card_le_one_iff_eq_bot
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [Finite ↥H], Nat.card ↥H ≤ 1 ↔ H = ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Groupstatement and proof · cited by 6,238
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement and proof · cited by 844
- Nat.card_eq_fintype_cardproof · cited by 200
- Fintype.card_uniqueproof · cited by 59
- Subgroup.eq_bot_of_card_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.one_lt_card_iff_ne_botproof · cited by 3