Theorems · Theorem · group theory
Subgroup.bot_or_nontrivial
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G), H = ⊥ ∨ Nontrivial ↥HA subgroup is either the trivial subgroup or nontrivial.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Nontrivialstatement and proof · cited by 2,416
- Subgroup.nontrivial_iff_ne_botproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.bot_or_exists_ne_oneproof · cited by 3
- Subgroup.SchurZassenhausInduction.step7proof · cited by 0
- LinearOrderedCommGroup.Subgroup.genLTOne_unique_of_zpowers_eqproof · cited by 0