Theorems · Theorem · field theory
Polynomial.natDegree_zero
∀ {R : Type u} [inst : Semiring R], Polynomial.natDegree 0 = 0- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 24 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.natDegreestatement · cited by 1,105
Cited by24
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_of_subsingletonproof · cited by 21
- Polynomial.natDegree_expandproof · cited by 7
- Polynomial.natDegree_divByMonicproof · cited by 5
- Polynomial.natTrailingDegree_le_natDegreeproof · cited by 4
- Polynomial.derivative_eq_zeroproof · cited by 4
- Polynomial.natDegree_modByMonic_ltproof · cited by 4
- Polynomial.natDegree_derivative_ltproof · cited by 4
- Polynomial.comp_eq_zero_iffproof · cited by 3
- Polynomial.natDegree_comp_leproof · cited by 2
- RingHom.isIntegralElem_leadingCoeff_mulproof · cited by 2
- finrank_quotient_span_eq_natDegreeproof · cited by 2
- MvPolynomial.natDegree_optionEquivLeftproof · cited by 2