Theorems · Theorem · field theory
Polynomial.natDegree_derivative_lt
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R},
p.natDegree ≠ 0 → (Polynomial.derivative p).natDegree < p.natDegree- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 110 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- eq_or_neproof · cited by 1,117
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.derivativestatement and proof · cited by 331
- Ne.bot_ltproof · cited by 116
- Polynomial.natDegree_zeroproof · cited by 24
- Polynomial.natDegree_lt_natDegree_iffproof · cited by 7
- Polynomial.degree_derivative_ltproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.iterate_derivative_eq_zeroproof · cited by 3
- Polynomial.separable_iff_derivative_ne_zeroproof · cited by 2
- Polynomial.natDegree_derivative_leproof · cited by 2
- Polynomial.iterate_derivative_eq_zero_of_degree_ltproof · cited by 1