Theorems · Theorem · group theory
add_zsmul
∀ {G : Type u_3} [inst : AddGroup G] (a : G) (m n : ℤ), (m + n) • a = m • a + n • a- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- add_zeroproof · cited by 2,707
- add_assocproof · cited by 746
- zero_nsmulproof · cited by 137
- ofNat_zsmulproof · cited by 24
- Int.induction_onproof · cited by 21
- add_one_zsmulproof · cited by 19
- sub_one_zsmulproof · cited by 3
Cited by22
Results whose statement or proof uses this declaration.
- sub_zsmulproof · cited by 12
- zmultiplesHomproof · cited by 7
- AddSubgroup.mem_closure_singletonproof · cited by 6
- one_add_zsmulproof · cited by 4
- fourier_addproof · cited by 3
- gcd_nsmul_eq_zeroproof · cited by 3
- mapClusterPt_self_zsmul_atTop_nsmulproof · cited by 3
- mod_addOrderOf_zsmulproof · cited by 3
- AddAction.zsmul_mod_period_vaddproof · cited by 3
- AddSubgroup.exists_nsmul_mem_of_index_ne_zeroproof · cited by 2
- AddConstMapClass.rel_map_of_Iccproof · cited by 2
- LinearOrderedAddCommGroup.isAddCyclic_iff_nonempty_equiv_intproof · cited by 2