Theorems · Theorem · group theory
add_one_zsmul
∀ {G : Type u_3} [inst : AddGroup G] (a : G) (n : ℤ), (n + 1) • a = n • a + a- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- neg_add_cancelproof · cited by 256
- neg_add_revproof · cited by 236
- zero_nsmulproof · cited by 137
- natCast_zsmulproof · cited by 118
- neg_add_cancel_rightproof · cited by 75
- succ_nsmulproof · cited by 65
- one_nsmulproof · cited by 63
- negSucc_zsmulproof · cited by 45
- neg_zsmulproof · cited by 41
- succ_nsmul'proof · cited by 25
- ofNat_zsmulproof · cited by 24
Cited by19
Results whose statement or proof uses this declaration.
- add_zsmulproof · cited by 21
- zsmul_left_strictMonoproof · cited by 8
- existsUnique_add_zsmul_mem_Iocproof · cited by 7
- Set.pairwise_disjoint_Ioc_add_zsmulproof · cited by 3
- sub_one_zsmulproof · cited by 3
- existsUnique_zsmul_near_of_pos'proof · cited by 3
- AddSubgroup.exists_isLeast_posproof · cited by 2
- ContinuousMap.periodic_tsum_comp_add_zsmulproof · cited by 2
- AddSubgroup.cyclic_of_minproof · cited by 2
- zsmul_left_monoproof · cited by 2
- AddCommGroup.modEq_iff_toIocMod_eq_rightproof · cited by 2
- Set.pairwise_disjoint_Ico_add_zsmulproof · cited by 2