Theorems · Theorem · group theory
AddSubmonoidClass.coe_finsetSum
∀ {B : Type u_3} {S : B} {ι : Type u_4} {M : Type u_5} [inst : AddCommMonoid M] [inst_1 : SetLike B M]
[inst_2 : AddSubmonoidClass B M] (f : ι → ↥S) (s : Finset ι), ↑(∑ i ∈ s, f i) = ∑ i ∈ s, ↑(f i)- Cited by
- 15 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- SetLikestatement and proof · cited by 1,084
- map_sumproof · cited by 455
- AddSubmonoidClassstatement and proof · cited by 346
- AddSubmonoidClass.subtypeproof · cited by 12
Cited by15
Results whose statement or proof uses this declaration.
- AddSubgroup.val_finsetSumproof · cited by 4
- DirectSum.coe_mul_apply_eq_dfinsuppSumproof · cited by 4
- DirectSum.coe_mul_applyproof · cited by 3
- MvPolynomial.esymmAlgHom_fin_injectiveproof · cited by 2
- OrthonormalBasis.orthogonalProjectionOnto_eq_sum_rankOneproof · cited by 2
- Submodule.restrictScalars_image_smul_eqproof · cited by 2
- Ideal.homogeneous_spanproof · cited by 1
- Rep.coindToInd_indToCoindproof · cited by 1
- IsHomogeneous.subsemiringClosureproof · cited by 1
- Algebra.mem_ideal_map_adjoinproof · cited by 1
- ZLattice.sum_piFinset_Icc_rpow_leproof · cited by 1
- Polynomial.degreeLT.addLinearEquiv_symm_apply_inrproof · cited by 1