Theorems · Theorem · field theory
Polynomial.leadingCoeff_add_of_degree_lt
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, p.degree < q.degree → (p + q).leadingCoeff = q.leadingCoeff- Cited by
- 10 results in Mathlib
- Foundations
- Depth 92 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.
Cites12
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
- zero_addproof · cited by 2,366
- 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.leadingCoeffstatement · cited by 498
- Polynomial.coeff_addproof · cited by 77
- Polynomial.natDegree_eq_of_degree_eqproof · cited by 19
- Polynomial.degree_add_eq_right_of_degree_ltproof · cited by 9
- Polynomial.coeff_natDegree_eq_zero_of_degree_ltproof · cited by 3
Cited by10
Results whose statement or proof uses this declaration.
- Matrix.charpoly_monicproof · cited by 9
- Polynomial.tendsto_abv_eval₂_atTopproof · cited by 2
- Polynomial.Monic.add_of_leftproof · cited by 2
- Polynomial.Monic.add_of_rightproof · cited by 2
- Polynomial.leadingCoeff_divByMonic_of_monicproof · cited by 2
- Polynomial.leadingCoeff_linearproof · cited by 1
- Polynomial.leadingCoeff_add_of_degree_lt'proof · cited by 1
- Polynomial.leadingCoeff_cubicproof · cited by 1
- Polynomial.leadingCoeff_quadraticproof · cited by 1
- Polynomial.leadingCoeff_sub_of_degree_lt'proof · cited by 0