Theorems · Theorem · field theory
Polynomial.coeff_eq_zero_of_degree_lt
∀ {R : Type u} {n : ℕ} [inst : Semiring R] {p : Polynomial R}, p.degree < ↑n → p.coeff n = 0- Cited by
- 22 results in Mathlib
- Foundations
- Depth 64 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.
Cites7
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
- WithBotstatement · cited by 1,498
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.degreestatement and proof · cited by 643
- not_le_of_gtproof · cited by 97
- Polynomial.le_degree_of_ne_zeroproof · cited by 11
Cited by22
Results whose statement or proof uses this declaration.
- Polynomial.coeff_eq_zero_of_natDegree_ltproof · cited by 55
- Polynomial.eq_C_of_degree_le_zeroproof · cited by 20
- Polynomial.eq_X_add_C_of_degree_le_oneproof · cited by 5
- Polynomial.coeff_mul_degree_add_degreeproof · cited by 5
- Polynomial.monic_X_pow_addproof · cited by 3
- Polynomial.coeff_natDegree_eq_zero_of_degree_ltproof · cited by 3
- Polynomial.coeff_isUnit_isNilpotent_of_isUnitproof · cited by 2
- PowerSeries.IsWeierstrassDivision.isUnit_of_map_ne_zeroproof · cited by 2
- Polynomial.integralNormalization_mul_C_leadingCoeffproof · cited by 2
- Polynomial.eraseLead_add_of_degree_lt_leftproof · cited by 1
- Polynomial.eraseLead_add_of_degree_lt_rightproof · cited by 1
- minpoly.eq_of_linearIndependentproof · cited by 1