Theorems · Theorem · group theory
QuotientAddGroup.mk_nsmul
∀ {G : Type u_1} [inst : AddGroup G] (N : AddSubgroup G) [nN : N.Normal] (a : G) (n : ℕ), ↑(n • a) = n • ↑a- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 75 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.
Cites5
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.Quotientstatement · cited by 2,301
- QuotientAddGroup.mkstatement · cited by 348
- AddSubgroup.Normalstatement and proof · cited by 183
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.nsmul_index_memproof · cited by 3
- AddCircle.card_torsion_le_of_isSMulRegularproof · cited by 2
- AddCommGroup.isAddTorsion_quotient_range_nsmulAddMonoidHomproof · cited by 2
- QuotientAddGroup.mk_nat_mulproof · cited by 0