Theorems · Theorem · commutative algebra
MonomialOrder.leadingCoeff_mul
∀ {σ : Type u_1} {m : MonomialOrder σ} {R : Type u_2} [inst : CommSemiring R] [NoZeroDivisors R]
{f g : MvPolynomial σ R}, m.leadingCoeff (f * g) = m.leadingCoeff f * m.leadingCoeff gMultiplicativity of leading coefficients
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 91 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.
Cites13
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 and proof · cited by 5,255
- MvPolynomialstatement and proof · cited by 2,140
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- NoZeroDivisorsstatement and proof · cited by 545
- MvPolynomial.coeffproof · cited by 315
- MonomialOrderstatement and proof · cited by 199
- MonomialOrder.degreeproof · cited by 132
- MonomialOrder.leadingCoeffstatement and proof · cited by 72
- MonomialOrder.leadingCoeff_zeroproof · cited by 14
- MonomialOrder.coeff_mul_of_degree_addproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- MonomialOrder.sPolynomial_monomial_mulproof · cited by 3
- MonomialOrder.leadingTerm_mulproof · cited by 0