Theorems · Theorem · field theory
Polynomial.leadingCoeff_eraseLead_eq_nextCoeff
∀ {R : Type u_1} [inst : Semiring R] {f : Polynomial R}, f.nextCoeff ≠ 0 → f.eraseLead.leadingCoeff = f.nextCoeff- Defined in
- Mathlib.Algebra.Polynomial.EraseLead
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 112 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.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- LT.lt.neproof · cited by 872
- ne_of_gtproof · cited by 637
- Polynomial.leadingCoeffstatement · cited by 498
- Polynomial.eraseLeadstatement and proof · cited by 65
- Polynomial.nextCoeffstatement and proof · cited by 46
- Polynomial.eraseLead_coeff_of_neproof · cited by 7
- tsub_lt_selfproof · cited by 7
- Polynomial.natDegree_pos_of_nextCoeff_ne_zeroproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.nextCoeff_eq_zero_of_eraseLead_eq_zeroproof · cited by 5
- Polynomial.succ_signVariations_le_X_sub_C_mulproof · cited by 1
- Polynomial.succ_signVariations_X_sub_C_mul_monomialproof · cited by 0
- Polynomial.signVariations_eraseLeadproof · cited by 0
- Polynomial.signVariations_eraseLead_mul_X_sub_Cproof · cited by 0