Theorems · Theorem · commutative algebra
MvPolynomial.degreeOf_le_iff
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {n : σ} {f : MvPolynomial σ R} {d : ℕ},
MvPolynomial.degreeOf n f ≤ d ↔ ∀ m ∈ f.support, m n ≤ d- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 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.
Cites9
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
- Finsetstatement · cited by 13,712
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.supportstatement and proof · cited by 220
- MvPolynomial.degreeOfstatement · cited by 53
- Finset.sup_le_iffproof · cited by 25
- MvPolynomial.degreeOf_eq_supproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- MvPolynomial.degreeOf_le_totalDegreeproof · cited by 1
- MvPolynomial.restrictTotalDegree_le_restrictDegreeproof · cited by 0