Theorems · Theorem · group theory
Finset.prod_inv_distrib
∀ {ι : Type u_1} {G : Type u_5} {s : Finset ι} [inst : DivisionCommMonoid G] (f : ι → G),
∏ x ∈ s, (f x)⁻¹ = (∏ x ∈ s, f x)⁻¹- Cited by
- 13 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- 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.
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement · cited by 2,356
- DivisionCommMonoidstatement and proof · cited by 80
- Multiset.prod_map_invproof · cited by 2
Cited by13
Results whose statement or proof uses this declaration.
- Complex.one_div_sub_pow_hasFPowerSeriesOnBall_zeroproof · cited by 3
- PeriodPair.summable_weierstrassPExceptSummandproof · cited by 3
- HasProd.inv₀proof · cited by 3
- Polynomial.div_prod_eq_quo_add_sum_rem_divproof · cited by 2
- BoundingSieve.selbergTerms_applyproof · cited by 2
- Real.harm_mean_le_geom_mean_weightedproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_singleproof · cited by 1
- dist_prod_prod_le_of_leproof · cited by 1
- Lagrange.leadingCoeff_basisproof · cited by 1
- Lagrange.nodalWeight_eq_eval_nodal_erase_invproof · cited by 1
- MeromorphicOn.exists_canonicalDecompproof · cited by 1
- BoundingSieve.inv_selbergTerms_eq_sum_divisors_moebius_nuproof · cited by 1