Theorems · Theorem · group theory
AddSubgroup.nsmul_index_mem
∀ {G : Type u_6} [inst : AddGroup G] (H : AddSubgroup G) [H.Normal] (g : G), H.index • g ∈ H- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- HasQuotient.Quotientproof · cited by 2,301
- QuotientAddGroup.mkproof · cited by 348
- AddSubgroup.Normalstatement and proof · cited by 183
- AddSubgroup.indexstatement and proof · cited by 104
- QuotientAddGroup.eq_zero_iffproof · cited by 19
- QuotientAddGroup.mk_nsmulproof · cited by 4
- card_nsmul_eq_zero'proof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.finrank_eq_of_finiteIndexproof · cited by 1
- Submodule.finiteQuotient_iffproof · cited by 1
- AddSubgroup.nsmul_relIndex_memproof · cited by 1