Theorems · Theorem · field theory
Polynomial.le_degree_of_ne_zero
∀ {R : Type u} {n : ℕ} [inst : Semiring R] {p : Polynomial R}, p.coeff n ≠ 0 → ↑n ≤ p.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 63 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.
Cites8
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
- WithBotstatement and proof · cited by 1,498
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.degreestatement and proof · cited by 643
- Finset.le_supproof · cited by 112
- Polynomial.mem_support_iffproof · cited by 30
- Nat.cast_withBotproof · cited by 15
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.coeff_eq_zero_of_degree_ltproof · cited by 22
- Polynomial.le_natDegree_of_ne_zeroproof · cited by 14
- Polynomial.degree_mul'proof · cited by 13
- Polynomial.degree_map_eq_of_leadingCoeff_ne_zeroproof · cited by 9
- Polynomial.natDegree_expandproof · cited by 7
- Polynomial.degree_eq_of_le_of_coeff_ne_zeroproof · cited by 4
- Polynomial.trinomial_natDegreeproof · cited by 4
- Polynomial.degree_le_degreeproof · cited by 3
- Polynomial.degree_shiftedLegendreproof · cited by 1
- Polynomial.le_degree_of_mem_suppproof · cited by 0
- Polynomial.degree_sum_eq_of_linearIndepOnproof · cited by 0