Theorems · Theorem · commutative algebra
MvPolynomial.degreeOf_mul_X_self
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (j : σ) (f : MvPolynomial σ R),
MvPolynomial.degreeOf j (f * MvPolynomial.X j) ≤ MvPolynomial.degreeOf j f + 1- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 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.
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 · cited by 5,255
- LE.le.transproof · cited by 3,151
- MvPolynomialstatement and proof · cited by 2,140
- MvPolynomial.Xstatement and proof · cited by 552
- Multiset.countproof · cited by 302
- MvPolynomial.degreeOfstatement · cited by 53
- MvPolynomial.degreesproof · cited by 51
- Multiset.count_addproof · cited by 23
- Multiset.count_le_of_leproof · cited by 12
- MvPolynomial.degrees_mul_leproof · cited by 6
- Multiset.count_singleton_selfproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- MvPolynomial.degreeOf_mul_X_eq_degreeOf_add_one_iffproof · cited by 1