Theorems · Theorem · field theory
Polynomial.leadingCoeff_zero
∀ {R : Type u} [inst : Semiring R], Polynomial.leadingCoeff 0 = 0- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 83 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.
Cites3
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 · cited by 5,681
- Polynomial.leadingCoeffstatement · cited by 498
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.modByMonic_eq_zero_iff_dvdproof · cited by 15
- Polynomial.degree_mul'proof · cited by 13
- Polynomial.leadingCoeff_mul_monicproof · cited by 6
- Polynomial.trailingCoeff_eq_zeroproof · cited by 5
- Polynomial.natDegree_pow'proof · cited by 4
- RingHom.isIntegralElem_localization_at_leadingCoeffproof · cited by 2
- Ideal.mem_leadingCoeffNthproof · cited by 1
- Polynomial.Chebyshev.leadingCoeff_eq_iff_of_forall_abs_le_oneproof · cited by 0