Theorems · Theorem · group theory
Finset.prod_pow_eq_pow_sum
∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] (s : Finset ι) (f : ι → ℕ) (a : M),
∏ i ∈ s, a ^ f i = a ^ ∑ i ∈ s, f i- Cited by
- 18 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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.sumstatement and proof · cited by 5,195
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- pow_zeroproof · cited by 1,094
- pow_addproof · cited by 315
- Finset.cons_inductionproof · cited by 85
- Finset.sum_consproof · cited by 84
- Finset.prod_consproof · cited by 60
Cited by18
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.norm_smulproof · cited by 5
- Subgroup.transferFocal_eq_powproof · cited by 2
- MonoidHom.transfer_eq_powproof · cited by 2
- MonoidHom.transfer_eq_pow_auxproof · cited by 2
- FormalMultilinearSeries.comp_summable_nnrealproof · cited by 2
- IsNonarchimedean.eval_mvPolynomial_leproof · cited by 1
- FormalMultilinearSeries.radius_right_inv_pos_of_radius_pos_aux1proof · cited by 1
- Algebra.discr_powerBasis_eq_prod''proof · cited by 1
- AlgebraicGeometry.Proj.valuativeCriterion_existence_auxproof · cited by 1
- Polynomial.resultant_prod_rightproof · cited by 1
- NumberField.mixedEmbedding.fundamentalCone.prod_expMapBasis_powproof · cited by 1
- AbsoluteValue.eval_mvPolynomial_leproof · cited by 1