Theorems · Theorem · field theory
Polynomial.natDegree_derivative
∀ {R : Type u} [inst : Semiring R] [IsAddTorsionFree R] (p : Polynomial R),
(Polynomial.derivative p).natDegree = p.natDegree - 1- Defined in
- Mathlib.Algebra.Polynomial.Derivative
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIsAddTorsionFree
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Nat.cast_oneproof · cited by 2,501
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.degreeproof · cited by 643
- Polynomial.derivativestatement · cited by 331
- IsAddTorsionFreestatement and proof · cited by 155
- WithBot.unbotDproof · cited by 49
- Nat.cast_tsubproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_derivativeproof · cited by 0