Theorems · Theorem · ring theory
Finsupp.sum_embDomain
∀ {α : Type u_1} {β : Type u_7} {M : Type u_8} {N : Type u_10} [inst : Zero M] [inst_1 : AddCommMonoid N] {v : α →₀ M}
{f : α ↪ β} {g : β → M → N}, (Finsupp.embDomain f v).sum g = v.sum fun a b => g (f a) b- Cited by
- 6 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement and proof · cited by 5,255
- Finset.sumproof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Function.Embeddingstatement and proof · cited by 988
- Finsupp.supportproof · cited by 828
- Finsupp.sumstatement and proof · cited by 481
- Finset.sum_mapproof · cited by 115
- Finsupp.embDomainstatement and proof · cited by 69
- Finsupp.embDomain_apply_selfproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- Finsupp.sum_mapDomain_index_injproof · cited by 4
- Module.Basis.maximalproof · cited by 1
- MvPolynomial.totalDegree_coeff_optionEquivLeft_add_leproof · cited by 1
- MvPolynomial.irreducible_sumSMulXSMulYproof · cited by 0
- MvPolynomial.totalDegree_coeff_optionEquivLeft_leproof · cited by 0
- BoundedContinuousFunction.star_mem_range_charAlgHomproof · cited by 0