Theorems · Theorem · field theory
Polynomial.eraseLead_coeff_of_ne
∀ {R : Type u_1} [inst : Semiring R] {f : Polynomial R} (i : ℕ), i ≠ f.natDegree → f.eraseLead.coeff i = f.coeff i- Defined in
- Mathlib.Algebra.Polynomial.EraseLead
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 71 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.
Cites6
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.eraseLeadstatement · cited by 65
- Polynomial.eraseLead_coeffproof · cited by 6
Cited by7
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_eraseLead_eq_nextCoeffproof · cited by 5
- Polynomial.coeffList_eraseLeadproof · cited by 4
- Polynomial.isUnit_of_coeff_isUnit_isNilpotentproof · cited by 2
- Polynomial.natDegree_eraseLeadproof · cited by 2
- Polynomial.natDegree_eraseLead_le_of_nextCoeff_eq_zeroproof · cited by 1
- Polynomial.leadingCoeff_cons_eraseLeadproof · cited by 0
- IsAlmostIntegral.coeffproof · cited by 0