Theorems · Theorem · group theory
mul_zpow
∀ {α : Type u_1} [inst : DivisionCommMonoid α] (a b : α) (n : ℤ), (a * b) ^ n = a ^ n * b ^ n- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext
- Assumes
- DivisionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- zpow_natCastproof · cited by 271
- mul_powproof · cited by 220
- zpow_negSuccproof · cited by 92
- DivisionCommMonoidstatement and proof · cited by 80
- mul_invproof · cited by 50
Cited by13
Results whose statement or proof uses this declaration.
- zpowGroupHomproof · cited by 12
- MeromorphicAt.meromorphicTrailingCoeffAt_zpowproof · cited by 5
- div_zpowproof · cited by 4
- meromorphicOrderAt_zpowproof · cited by 4
- UpperHalfPlane.petersson_slashproof · cited by 3
- MeromorphicNFAt.zpowproof · cited by 2
- NumberField.exists_ne_zero_mem_ideal_of_norm_le_mul_sqrt_discrproof · cited by 2
- MeromorphicNFAt.comp_analyticAtproof · cited by 1
- SlashInvariantForm.wt_eq_zero_of_eq_constproof · cited by 1
- Polynomial.Chebyshev.one_le_negOnePow_mul_eval_T_realproof · cited by 0
- Polynomial.Chebyshev.one_lt_negOnePow_mul_eval_T_realproof · cited by 0
- circleMap_zero_zpowproof · cited by 0