Theorems · Theorem · group theory
AddSubgroup.isAddCyclic_iff_exists_zmultiples_eq_top
∀ {α : Type u_1} [inst : AddGroup α] (H : AddSubgroup α), IsAddCyclic ↥H ↔ ∃ g, AddSubgroup.zmultiples g = H- Cited by
- 4 results in Mathlib
- Foundations
- Depth 76 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubgroup.zmultiplesstatement and proof · cited by 493
- AddSubgroup.mapproof · cited by 189
- AddSubgroup.subtypeproof · cited by 82
- IsAddCyclicstatement · cited by 55
- AddSubgroup.range_subtypeproof · cited by 16
- AddMonoidHom.range_eq_mapproof · cited by 15
- AddSubgroup.mem_zmultiplesproof · cited by 10
- AddMonoidHom.map_zmultiplesproof · cited by 6
- AddSubgroup.map_subtype_injproof · cited by 4
- isAddCyclic_iff_exists_zmultiples_eq_topproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.strictPeriods_eq_zmultiples_strictWidthInftyproof · cited by 4
- LinearOrderedAddCommGroup.Subgroup.exists_neg_generatorproof · cited by 2
- AddSubgroup.discrete_iff_addCyclicproof · cited by 1
- AddSubgroup.le_zmultiples_iffproof · cited by 0