Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_mul_of_isDomain
∀ {R : Type u_1} {σ : Type u_2} [inst : CommSemiring R] [NoZeroDivisors R] {f g : MvPolynomial σ R},
f ≠ 0 → g ≠ 0 → (f * g).totalDegree = f.totalDegree + g.totalDegree- Cited by
- 3 results in Mathlib
- Foundations
- Depth 98 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- LinearOrderproof · cited by 8,572
- Finsuppstatement · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- map_addproof · cited by 964
- NoZeroDivisorsstatement and proof · cited by 545
- MonomialOrderproof · cited by 199
- MonomialOrder.degreeproof · cited by 132
- WellFoundedGTproof · cited by 114
- Finsupp.degreeproof · cited by 94
- MvPolynomial.totalDegreestatement · cited by 76
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_le_of_dvd_of_isDomainproof · cited by 1
- MvPolynomial.irreducible_of_forall_totalDegree_leproof · cited by 1
- MvPolynomial.irreducible_of_totalDegree_eq_oneproof · cited by 1