Theorems · Theorem · commutative algebra
MonomialOrder.degree_mul
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] [NoZeroDivisors R]
{f g : MvPolynomial σ R}, f ≠ 0 → g ≠ 0 → m.degree (f * g) = m.degree f + m.degree gMonomial degree of product
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 90 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.
Cites7
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
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreestatement · cited by 132
- MonomialOrder.degree_mul_of_mul_leadingCoeff_ne_zeroproof · cited by 5
Cited by9
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_mul_of_isDomainproof · cited by 3
- MonomialOrder.sPolynomial_monomial_mulproof · cited by 3
- MonomialOrder.leadingCoeff_mulproof · cited by 2
- MonomialOrder.degree_leadingTerm_mulproof · cited by 1
- MonomialOrder.degree_lt_of_left_ne_zero_of_degree_mul_ltproof · cited by 1
- MonomialOrder.degree_mul'proof · cited by 1
- MonomialOrder.degree_mul_lt_iff_left_lt_of_ne_zeroproof · cited by 0
- MonomialOrder.sPolynomial_leadingTerm_mul'proof · cited by 0
- MonomialOrder.sPolynomial_monomial_mul'proof · cited by 0