Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_finsetSum
∀ {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).totalDegree- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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 and proof · cited by 5,195
- LE.le.transproof · cited by 3,151
- MvPolynomialstatement and proof · cited by 2,140
- le_rflproof · cited by 1,558
- Finset.supstatement and proof · cited by 530
- zero_leproof · cited by 382
- Finset.consproof · cited by 221
- Finset.cons_inductionproof · cited by 85
- Finset.sum_consproof · cited by 84
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_finsetSum_leproof · cited by 1
- MvPolynomial.totalDegree_finset_sumproof · cited by 0