Theorems · Theorem · group theory
AddSubgroup.exists_nsmul_mem_of_relIndex_ne_zero
∀ {G : Type u_1} [inst : AddGroup G] {H K : AddSubgroup G},
H.relIndex K ≠ 0 → ∀ {a : G}, a ∈ K → ∃ n, 0 < n ∧ n ≤ H.relIndex K ∧ n • a ∈ H ⊓ K- Defined in
- Mathlib.GroupTheory.Index
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites9
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.indexproof · cited by 104
- AddSubgroup.addSubgroupOfproof · cited by 87
- AddSubgroup.relIndexstatement and proof · cited by 67
- nsmul_memproof · cited by 26
- AddSubgroup.mem_addSubgroupOfproof · cited by 14
- AddSubgroup.mem_infproof · cited by 8
- AddSubgroup.exists_nsmul_mem_of_index_ne_zeroproof · cited by 2
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