Theorems · Theorem · field theory
Polynomial.ne_zero_of_natDegree_gt
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {n : ℕ}, n < p.natDegree → p ≠ 0- Cited by
- 13 results in Mathlib
- Foundations
- Depth 83 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.
Cites3
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
Cited by13
Results whose statement or proof uses this declaration.
- Polynomial.degree_lt_degreeproof · cited by 14
- Polynomial.natDegree_compproof · cited by 13
- FiniteField.X_pow_card_sub_X_ne_zeroproof · cited by 4
- ascPochhammer_natDegreeproof · cited by 2
- Lagrange.nodal_ne_zeroproof · cited by 1
- descPochhammer_natDegreeproof · cited by 1
- WeierstrassCurve.preΨ'_ne_zeroproof · cited by 1
- WeierstrassCurve.preΨ₄_ne_zeroproof · cited by 0
- WeierstrassCurve.Ψ₂Sq_ne_zeroproof · cited by 0
- WeierstrassCurve.Φ_ne_zeroproof · cited by 0
- WeierstrassCurve.Ψ₃_ne_zeroproof · cited by 0
- Polynomial.leadingCoeff_cons_eraseLeadproof · cited by 0