Theorems · Theorem · field theory
Polynomial.degree_add_le_of_degree_le
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R} {n : ℕ}, p.degree ≤ ↑n → q.degree ≤ ↑n → (p + q).degree ≤ ↑n- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 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.
Cites7
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
- LE.le.transproof · cited by 3,151
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- max_leproof · cited by 71
- Polynomial.degree_add_leproof · cited by 14
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.degree_linear_leproof · cited by 5
- Polynomial.degree_quadratic_leproof · cited by 4
- Polynomial.degree_cubic_leproof · cited by 3