Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_le_of_dvd_of_isDomain
∀ {R : Type u_1} {σ : Type u_2} [inst : CommSemiring R] [NoZeroDivisors R] {f g : MvPolynomial σ R},
f ∣ g → g ≠ 0 → f.totalDegree ≤ g.totalDegree- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- NoZeroDivisorsstatement and proof · cited by 545
- MvPolynomial.totalDegreestatement and proof · cited by 76
- MvPolynomial.totalDegree_mul_of_isDomainproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.dvd_C_iff_existsproof · cited by 1