Theorems · Theorem · group theory
isAddCyclic_iff_exists_zmultiples_eq_top
∀ {α : Type u_1} [inst : AddGroup α], IsAddCyclic α ↔ ∃ g, AddSubgroup.zmultiples g = ⊤- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement · cited by 9,680
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement · cited by 3,232
- AddSubgroup.zmultiplesstatement and proof · cited by 493
- IsAddCyclicstatement and proof · cited by 55
- AddSubgroup.mem_zmultiples_iffproof · cited by 11
- AddSubgroup.eq_top_iff'proof · cited by 11
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.isAddCyclic_iff_exists_zmultiples_eq_topproof · cited by 4
- isAddCyclic_iff_exists_addOrderOf_eq_natCardproof · cited by 2
- IsAddCyclic.card_nsmulAddMonoidHom_rangeproof · cited by 1
- AddSubgroup.discrete_iff_addCyclicproof · cited by 1