Theorems · Theorem · group theory
zpow_add
∀ {G : Type u_3} [inst : Group G] (a : G) (m n : ℤ), a ^ (m + n) = a ^ m * a ^ n- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 40 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- mul_assocproof · cited by 1,667
- pow_zeroproof · cited by 1,094
- zpow_ofNatproof · cited by 144
- Int.induction_onproof · cited by 21
- zpow_add_oneproof · cited by 18
- zpow_sub_oneproof · cited by 3
Cited by40
Results whose statement or proof uses this declaration.
- Int.negOnePow_addproof · cited by 25
- zpow_subproof · cited by 15
- ModularGroup.coe_T_zpowproof · cited by 9
- IsPrimitiveRoot.pow_of_coprimeproof · cited by 8
- zpow_mod_orderOfproof · cited by 6
- Equiv.Perm.IsCycle.sameCycleproof · cited by 4
- Equiv.Perm.sameCycle_zpow_leftproof · cited by 4
- zpow_one_addproof · cited by 3
- Subgroup.mem_closure_singletonproof · cited by 3
- MulAction.zpow_mod_period_smulproof · cited by 3
- IsPrimitiveRoot.eq_pow_of_mem_rootsOfUnityproof · cited by 3
- Equiv.Perm.SameCycle.transproof · cited by 2