Theorems · Theorem · field theory
Polynomial.natDegree_le_pred
∀ {R : Type u} {n : ℕ} [inst : Semiring R] {p : Polynomial R}, p.natDegree ≤ n → p.coeff n = 0 → p.natDegree ≤ n - 1- Cited by
- 1 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.
Cites7
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
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.coeff_natDegreeproof · cited by 16
- Nat.le_succ_iff_eq_or_leproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_eraseLead_le_of_nextCoeff_eq_zeroproof · cited by 1