Theorems · Theorem · group theory
zpow_mul
∀ {α : Type u_1} [inst : DivisionMonoid α] (a : α) (m n : ℤ), a ^ (m * n) = (a ^ m) ^ n- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- DivisionMonoid
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.
- inv_invproof · cited by 494
- zpow_natCastproof · cited by 271
- pow_mulproof · cited by 210
- DivisionMonoidstatement and proof · cited by 201
- zpow_negproof · cited by 198
- inv_powproof · cited by 140
- zpow_negSuccproof · cited by 92
- inv_injproof · cited by 25
Cited by27
Results whose statement or proof uses this declaration.
- Int.cast_negOnePowproof · cited by 10
- IsPrimitiveRoot.pow_of_coprimeproof · cited by 8
- zpow_mod_orderOfproof · cited by 6
- zpow_mul'proof · cited by 4
- meromorphicOrderAt_zpowproof · cited by 4
- Equiv.Perm.IsCycle.of_powproof · cited by 3
- MonoidHom.map_cyclicproof · cited by 3
- IsPrimitiveRoot.eq_pow_of_mem_rootsOfUnityproof · cited by 3
- Even.neg_zpowproof · cited by 2
- zpow_eq_zpow_emodproof · cited by 2
- Equiv.Perm.IsCycleOn.exists_pow_eqproof · cited by 2
- zpow_pow_orderOfproof · cited by 2