Theorems · Theorem · group theory
AddSubgroup.le_zmultiples_iff
∀ {G : Type u_2} [inst : AddGroup G] (g : G) (H : AddSubgroup G),
H ≤ AddSubgroup.zmultiples g ↔ ∃ n, H = AddSubgroup.zmultiples (n • g)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
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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
- natCast_zsmulproof · cited by 118
- neg_zsmulproof · cited by 41
- AddSubgroup.mem_zmultiples_iffproof · cited by 11
- AddSubgroup.mem_zmultiplesproof · cited by 10
- AddSubgroup.zmultiples_negproof · cited by 6
- AddSubgroup.isAddCyclic_iff_exists_zmultiples_eq_topproof · cited by 4
- AddSubgroup.nsmul_mem_zmultiplesproof · cited by 1
- AddSubgroup.zmultiples_le_of_memproof · cited by 1
- AddSubgroup.isAddCyclic_of_leproof · cited by 1
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