Theorems · Theorem · field theory
Polynomial.natDegree_eraseLead_le_of_nextCoeff_eq_zero
∀ {R : Type u_1} [inst : Semiring R] {f : Polynomial R}, f.nextCoeff = 0 → f.eraseLead.natDegree ≤ f.natDegree - 2- Defined in
- Mathlib.Algebra.Polynomial.EraseLead
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 111 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.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- LT.lt.neproof · cited by 872
- zero_lt_oneproof · cited by 598
- zero_tsubproof · cited by 100
- Polynomial.eraseLeadstatement · cited by 65
- Polynomial.natDegree_Cproof · cited by 59
- Polynomial.nextCoeffstatement and proof · cited by 46
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.eraseLead_mul_eq_mul_eraseLead_of_nextCoeff_zeroproof · cited by 1