Theorems · Theorem · group theory
AddSubgroup.nontrivial_iff_ne_bot
∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G), Nontrivial ↥H ↔ H ≠ ⊥- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botstatement and proof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Nontrivialstatement · cited by 2,416
- AddSubgroup.eq_bot_iff_forallproof · cited by 11
- AddSubgroup.nontrivial_iff_exists_ne_zeroproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- LinearOrderedAddCommGroup.Subgroup.exists_neg_generatorproof · cited by 2
- AddSubgroup.bot_or_nontrivialproof · cited by 2
- AddSubgroup.isSimpleAddGroup_iffproof · cited by 0
- AddSubgroup.ne_bot_iff_exists_ne_zeroproof · cited by 0