Theorems · Theorem · field theory
Polynomial.degree_add_eq_of_leadingCoeff_add_ne_zero
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R},
p.leadingCoeff + q.leadingCoeff ≠ 0 → (p + q).degree = max p.degree q.degree- Cited by
- 1 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.
Cites20
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_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- WithBotstatement and proof · 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 and proof · cited by 498
- le_of_not_gtproof · cited by 430
- lt_trichotomyproof · cited by 178
- Polynomial.coeff_addproof · cited by 77
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_add_of_degree_eqproof · cited by 1