Theorems · Theorem · group theory
Subgroup.one_lt_card_iff_ne_bot
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) [Finite ↥H], 1 < Nat.card ↥H ↔ H ≠ ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Finite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 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 · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- Finitestatement and proof · cited by 3,029
- Nat.cardstatement · cited by 844
- Iff.notproof · cited by 489
- lt_iff_not_geproof · cited by 22
- Subgroup.card_le_one_iff_eq_botproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IsPGroup.bot_lt_centerproof · cited by 2
- IsPGroup.isNilpotentproof · cited by 1
- Equiv.Perm.subgroup_eq_top_of_nontrivialproof · cited by 0