Theorems · Theorem · field theory
Polynomial.sumIDeriv_apply_of_le
∀ {R : Type u_1} [inst : Semiring R] {p : Polynomial R} {n : ℕ},
p.natDegree ≤ n → Polynomial.sumIDeriv p = ∑ i ∈ Finset.range (n + 1), (⇑Polynomial.derivative)^[i] p- Cited by
- 2 results in Mathlib
- Foundations
- Depth 117 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.
Cites13
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
- Finset.sumstatement · cited by 5,195
- Finset.rangestatement · cited by 1,341
- Polynomial.natDegreestatement and proof · cited by 1,105
- Nat.iteratestatement · cited by 740
- Polynomial.derivativestatement · cited by 331
- Finsupp.sum_of_support_subsetproof · cited by 21
- Polynomial.sumIDerivstatement · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.sumIDeriv_mapproof · cited by 1
- Polynomial.sumIDeriv_derivativeproof · cited by 0