Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_finset_sum
Deprecated since 2026-04-08Use MvPolynomial.totalDegree_finsetSum instead.
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {ι : Type u_3} (s : Finset ι) (f : ι → MvPolynomial σ R),
(s.sum f).totalDegree ≤ s.sup fun i => (f i).totalDegreeAlias of MvPolynomial.totalDegree_finsetSum.
- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- CommSemiringstatement · cited by 10,911
- Finsuppstatement · cited by 5,255
- Finset.sumstatement · cited by 5,195
- MvPolynomialstatement · cited by 2,140
- Finset.supstatement · cited by 530
- MvPolynomial.totalDegreestatement · cited by 76
- MvPolynomial.totalDegree_finsetSumproof · cited by 2
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