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Theorems · Theorem · group theory

Prod.fst_sum

∀ {ι : Type u_1} {M : Type u_3} {N : Type u_4} [inst : AddCommMonoid M] [inst_1 : AddCommMonoid N] {s : Finset ι}
  {f : ι → M × N}, (∑ c ∈ s, f c).1 = ∑ c ∈ s, (f c).1
Defined in
Mathlib.Algebra.BigOperators.Pi
Cited by
5 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
AddCommMonoidAddCommMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ConvexOn.map_centerMass_le · cited by 4ConvexOn.map_centerMass_leLinearMap.fst_prodOfFinsuppNat · cited by 1LinearMap.fst_prodOfFinsu…mk_mem_convexHull_prod · cited by 1mk_mem_convexHull_prodModule.Basis.prod_parallelepiped · cited by 1Basis.prod_parallelepipedTrivSqZeroExt.fst_sum · cited by 0TrivSqZeroExt.fst_sumFinset · cited by 13712FinsetAddCommMonoid · cited by 12281AddCommMonoidFinset.sum · cited by 5195Finset.summap_sum · cited by 455map_sumAddMonoidHom.fst · cited by 39AddMonoidHom.fstProd.fst_sumCITED BYCITES

Cites5

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Cited by5

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