Theorems · Theorem · commutative algebra
MvPolynomial.totalDegree_add
∀ {R : Type u} {σ : Type u_1} [inst : CommSemiring R] (a b : MvPolynomial σ R),
(a + b).totalDegree ≤ max a.totalDegree b.totalDegree- Defined in
- Mathlib.Algebra.MvPolynomial.Degrees
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 82 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.
Cites6
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
- Finsupp.sumproof · cited by 481
- MvPolynomial.totalDegreestatement · cited by 76
- AddMonoidAlgebra.sup_support_coeff_add_leproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.totalDegree_finsetSumproof · cited by 2
- MvPolynomial.totalDegree_subproof · cited by 2
- MvPolynomial.totalDegree_add_eq_left_of_totalDegree_ltproof · cited by 1