Theorems · Theorem · field theory
Polynomial.coeff_eq_zero_of_natDegree_lt
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {n : ℕ}, p.natDegree < n → p.coeff n = 0- Cited by
- 55 results in Mathlib
- Foundations
- Depth 89 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.
Cites9
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
- WithBotproof · cited by 1,498
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffstatement · cited by 1,045
- Nat.cast_ltproof · cited by 80
- Polynomial.degree_eq_natDegreeproof · cited by 69
- WithBot.bot_lt_coeproof · cited by 37
- Polynomial.coeff_eq_zero_of_degree_ltproof · cited by 22
Cited by55
Results whose statement or proof uses this declaration.
- Polynomial.coeff_comp_degree_mul_degreeproof · cited by 7
- Polynomial.natDegree_expandproof · cited by 7
- Polynomial.coeff_contractproof · cited by 6
- Polynomial.coeffList_eraseLeadproof · cited by 4
- IsIntegral.coeffproof · cited by 4
- Polynomial.coeff_mirrorproof · cited by 4
- Polynomial.coeff_add_eq_left_of_ltproof · cited by 3
- Polynomial.norm_coeff_le_choose_mul_mahlerMeasureproof · cited by 3
- Polynomial.Monic.eq_X_pow_iff_natDegree_le_natTrailingDegreeproof · cited by 3
- Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_evalproof · cited by 3
- Polynomial.coeff_one_reverseproof · cited by 2
- Polynomial.isNilpotent_reflect_iffproof · cited by 2