Theorems · Theorem · group theory
Finset.prod_pow
∀ {ι : Type u_1} {M : Type u_3} [inst : CommMonoid M] (s : Finset ι) (n : ℕ) (f : ι → M),
∏ x ∈ s, f x ^ n = (∏ x ∈ s, f x) ^ n- Cited by
- 10 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
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
- CommMonoidstatement and proof · cited by 2,264
- Multiset.prod_map_powproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- Nat.dvd_prod_primeFactors_pow_selfproof · cited by 4
- IsArtinianRing.nilradical_pow_eq_iInfproof · cited by 3
- commProb_piproof · cited by 3
- Nat.prod_primeFactors_pow_totient_ediv_dvdproof · cited by 2
- IsCyclotomicExtension.Rat.discrproof · cited by 1
- Algebra.discr_powerBasis_eq_prodproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.prod_deriv_expMap_singleproof · cited by 1
- Complex.GammaSeq_mulproof · cited by 1
- Algebra.prod_embeddings_eq_finrank_powproof · cited by 1
- LinearMap.normDet_eq_prod_singularValuesproof · cited by 0