Theorems · Theorem · commutative algebra
MvPolynomial.degrees_mul_le
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] {p q : MvPolynomial σ R}, (p * q).degrees ≤ p.degrees + q.degrees- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 83 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.
- CommSemiringstatement and proof · cited by 10,911
- Finsuppstatement · cited by 5,255
- Multisetstatement · cited by 2,627
- MvPolynomialstatement and proof · cited by 2,140
- map_addproof · cited by 964
- MvPolynomial.degreesstatement · cited by 51
- Finsupp.toMultisetproof · cited by 44
- MvPolynomial.degrees_defproof · cited by 8
- AddMonoidAlgebra.supDegree_mul_leproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- MvPolynomial.vars_mulproof · cited by 6
- MvPolynomial.degreeOf_mul_X_selfproof · cited by 1
- MvPolynomial.degreeOf_C_mul_leproof · cited by 0
- MvPolynomial.degreeOf_mul_C_leproof · cited by 0
- MvPolynomial.degreeOf_mul_leproof · cited by 0
- MvPolynomial.degreesLE_addproof · cited by 0