Theorems · Theorem · group theory
mul_pow
∀ {M : Type u_4} [inst : CommMonoid M] (a b : M) (n : ℕ), (a * b) ^ n = a ^ n * b ^ n- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 220 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 70 definitions · uses propext
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
Cited by221
Results whose statement or proof uses this declaration.
- div_powproof · cited by 66
- powMonoidHomproof · cited by 35
- mul_zpowproof · cited by 12
- Complex.sin_sq_add_cos_sqproof · cited by 11
- IsPrimitiveRoot.pow_of_coprimeproof · cited by 8
- ProbabilityTheory.charFun_gaussianRealproof · cited by 7
- NNReal.sqrt_mulproof · cited by 6
- Real.sin_pi_over_two_pow_succproof · cited by 6
- IsLocalization.Away.of_associatedproof · cited by 6
- NumberField.mixedEmbedding.norm_smulproof · cited by 5
- EuclideanGeometry.inversion_inversionproof · cited by 5
- Finset.sum_mul_sq_le_sq_mul_sqproof · cited by 5
Showing the 200 most cited of 221.