Theorems · Theorem · field theory
Polynomial.degree_add_eq_left_of_degree_lt
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, q.degree < p.degree → (p + q).degree = p.degree- Cited by
- 14 results in Mathlib
- Foundations
- Depth 90 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.
Cites15
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_zeroproof · cited by 2,707
- le_antisymmproof · cited by 2,068
- WithBotstatement · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.coeff_addproof · cited by 77
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.degree_add_leproof · cited by 14
- Polynomial.ne_zero_of_degree_gtproof · cited by 13
Cited by14
Results whose statement or proof uses this declaration.
- Polynomial.degree_sub_eq_left_of_degree_ltproof · cited by 10
- Polynomial.degree_add_eq_right_of_degree_ltproof · cited by 9
- Polynomial.degree_cubicproof · cited by 3
- Polynomial.degree_quadraticproof · cited by 2
- Polynomial.degree_X_add_Cproof · cited by 2
- Polynomial.degree_X_pow_add_Cproof · cited by 2
- Polynomial.degree_sum_eq_of_disjointproof · cited by 2
- Polynomial.natDegree_add_eq_left_of_degree_ltproof · cited by 2
- Polynomial.degree_linearproof · cited by 1
- Polynomial.degree_divX_ltproof · cited by 1
- WittVector.RecursionMain.succNthDefiningPoly_degreeproof · cited by 1
- Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zeroproof · cited by 1