Theorems · Theorem · commutative algebra
MvPolynomial.support_sum
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {α : Type u_2} [inst_1 : DecidableEq σ] {s : Finset α}
{f : α → MvPolynomial σ R}, (∑ x ∈ s, f x).support ⊆ s.biUnion fun x => (f x).support- Defined in
- Mathlib.Algebra.MvPolynomial.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Finset.sumstatement · cited by 5,195
- MvPolynomialstatement and proof · cited by 2,140
- Finsupp.supportproof · cited by 828
- AddMonoidAlgebra.coeffproof · cited by 365
- MvPolynomial.supportstatement · cited by 220
- Finset.biUnionstatement and proof · cited by 217
- AddMonoidAlgebra.coeff_sumproof · cited by 6
- Finsupp.support_finsetSumproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.support_expand_subsetproof · cited by 2