Theorems · Theorem · field theory
Polynomial.two_le_natDegree_of_nextCoeff_eraseLead
∀ {R : Type u_1} [inst : Semiring R] {f : Polynomial R}, f.eraseLead ≠ 0 → f.nextCoeff = 0 → 2 ≤ f.natDegree- Defined in
- Mathlib.Algebra.Polynomial.EraseLead
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- add_zeroproof · cited by 2,707
- Polynomial.Xproof · cited by 1,639
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.eraseLeadstatement and proof · cited by 65
- Polynomial.nextCoeffstatement and proof · cited by 46
- Polynomial.natDegree_eq_zeroproof · cited by 14
- Polynomial.eraseLead_Cproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zeroproof · cited by 1