Theorems · Theorem · field theory
Polynomial.natDegree_eq_zero_of_derivative_eq_zero
Deprecated since 2026-06-03Use Polynomial.derivative_eq_zero instead.
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} [IsAddTorsionFree R],
Polynomial.derivative p = 0 → p.natDegree = 0Alias of the forward direction of Polynomial.derivative_eq_zero.
- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIsAddTorsionFree
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.derivativestatement · cited by 331
- IsAddTorsionFreestatement and proof · cited by 155
- Polynomial.derivative_eq_zeroproof · cited by 4
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