Theorems · Theorem · field theory
Polynomial.natDegree_eraseLead
∀ {R : Type u_1} [inst : Semiring R] {f : Polynomial R}, f.nextCoeff ≠ 0 → f.eraseLead.natDegree = f.natDegree - 1- Defined in
- Mathlib.Algebra.Polynomial.EraseLead
- Cited by
- 2 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.
Cites13
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
- LT.lt.neproof · cited by 872
- LE.le.antisymmproof · cited by 507
- Polynomial.eraseLeadstatement · cited by 65
- Polynomial.nextCoeffstatement and proof · cited by 46
- Polynomial.le_natDegree_of_ne_zeroproof · cited by 14
- Polynomial.eraseLead_natDegree_leproof · cited by 8
- Polynomial.eraseLead_coeff_of_neproof · cited by 7
- tsub_lt_selfproof · cited by 7
- Polynomial.nextCoeff_of_natDegree_posproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_eraseLead_eq_nextCoeffproof · cited by 5
- Polynomial.natDegree_eraseLead_add_oneproof · cited by 3