Theorems · Theorem · group theory
div_pow
∀ {α : Type u_1} [inst : DivisionCommMonoid α] (a b : α) (n : ℕ), (a / b) ^ n = a ^ n / b ^ n- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 66 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- DivisionCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- div_eq_mul_invproof · cited by 715
- mul_powproof · cited by 220
- inv_powproof · cited by 140
- DivisionCommMonoidstatement and proof · cited by 80
Cited by66
Results whose statement or proof uses this declaration.
- isLittleO_pow_pow_of_lt_leftproof · cited by 5
- Real.sqrtTwoAddSeries_step_downproof · cited by 5
- Real.sqrtTwoAddSeries_step_upproof · cited by 5
- InnerProductGeometry.angle_add_eq_arcsin_of_inner_eq_zeroproof · cited by 5
- InnerProductGeometry.angle_add_eq_arctan_of_inner_eq_zeroproof · cited by 4
- WeierstrassCurve.Jacobian.equiv_of_X_eq_of_Y_eqproof · cited by 4
- Complex.inv_one_add_tan_sqproof · cited by 4
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- FormalMultilinearSeries.div_le_radius_compContinuousLinearMapproof · cited by 3
- NNReal.sqrt_mul_le_half_addproof · cited by 3
- DoubleCentralizer.norm_fst_eq_sndproof · cited by 3
- FormalMultilinearSeries.isLittleO_of_lt_radiusproof · cited by 3