Theorems · Theorem · field theory
Polynomial.degree_add_eq_right_of_degree_lt
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, p.degree < q.degree → (p + q).degree = q.degree- Cited by
- 9 results in Mathlib
- Foundations
- Depth 91 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.
Cites6
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
- add_commproof · cited by 1,535
- WithBotstatement and proof · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.degree_add_eq_left_of_degree_ltproof · cited by 14
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_add_of_degree_ltproof · cited by 10
- Matrix.charpoly_degree_eq_dimproof · cited by 4
- Polynomial.degree_add_divByMonicproof · cited by 4
- Polynomial.degree_sub_eq_right_of_degree_ltproof · cited by 3
- Polynomial.degree_add_Cproof · cited by 2
- Polynomial.degree_sum_eq_of_disjointproof · cited by 2
- Polynomial.natDegree_add_eq_right_of_degree_ltproof · cited by 2
- Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zeroproof · cited by 1
- WeierstrassCurve.Affine.irreducible_polynomialproof · cited by 0