Theorems · Theorem · field theory
Polynomial.degree_add_le
∀ {R : Type u} [inst : Semiring R] (p q : Polynomial R), (p + q).degree ≤ max p.degree q.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement · cited by 1,498
- Finsupp.supportproof · cited by 828
- Polynomial.degreestatement · cited by 643
- WithBot.someproof · cited by 541
- AddMonoidAlgebra.coeffproof · cited by 365
- Polynomial.toFinsuppproof · cited by 64
- Finset.maxproof · cited by 50
- Polynomial.toFinsupp_addproof · cited by 5
- AddMonoidAlgebra.sup_support_coeff_add_leproof · cited by 5
Cited by14
Results whose statement or proof uses this declaration.
- Polynomial.degree_add_eq_left_of_degree_ltproof · cited by 14
- Polynomial.degree_sum_leproof · cited by 11
- Polynomial.degree_sub_lt_leftproof · cited by 9
- Polynomial.degree_sub_leproof · cited by 8
- Polynomial.natDegree_add_leproof · cited by 6
- Polynomial.monic_X_pow_addproof · cited by 3
- Polynomial.add_modByMonicproof · cited by 3
- Polynomial.degree_add_le_of_degree_leproof · cited by 3
- PowerSeries.IsWeierstrassDivisionAt.addproof · cited by 2
- Polynomial.cardPowDegree_anti_archimedeanproof · cited by 1
- WeierstrassCurve.Affine.CoordinateRing.degree_norm_smul_basisproof · cited by 1
- Polynomial.degree_list_sum_le_of_forall_degree_leproof · cited by 1