Theorems · Theorem · group theory
isAddCyclic_additive_iff
∀ {α : Type u_1} [inst : DivInvMonoid α], IsAddCyclic (Additive α) ↔ IsCyclic α- Cited by
- 3 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses Quot.sound
- Assumes
- DivInvMonoid
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.
- Additivestatement and proof · cited by 356
- IsCyclicstatement and proof · cited by 122
- DivInvMonoidstatement and proof · cited by 103
- IsAddCyclicstatement and proof · cited by 55
- IsAddCyclic.exists_zsmul_surjectiveproof · cited by 3
- IsCyclic.exists_zpow_surjectiveproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- not_isCyclic_prod_of_infinite_nontrivialproof · cited by 1
- LinearOrderedCommGroup.isCyclic_iff_not_denselyOrderedproof · cited by 0
- LinearOrderedCommGroup.isCyclic_iff_nonempty_equiv_intproof · cited by 0