Theorems · Theorem · field theory

Polynomial.divByMonic_add_X_sub_C_mul_derivative_divByMonic_eq_derivative

∀ {K : Type u_1} [inst : CommRing K] (f : Polynomial K) (a : K),
  f /ₘ (Polynomial.X - Polynomial.C a) +
      (Polynomial.X - Polynomial.C a) * Polynomial.derivative (f /ₘ (Polynomial.X - Polynomial.C a)) =
    Polynomial.derivative f

Defined in: Mathlib.Algebra.Polynomial.FieldDivision
Cited by: 1 results in Mathlib
Foundations: Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites19

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
CommRingstatement and proof · cited by 17,173
LinearMapstatement · cited by 10,215
RingHomstatement · cited by 10,189
Polynomialstatement and proof · cited by 5,681
one_mulproof · cited by 2,841
Polynomial.Xstatement and proof · cited by 1,639
Polynomial.Cstatement and proof · cited by 1,598
sub_zeroproof · cited by 938
Polynomial.derivativestatement and proof · cited by 331
Polynomial.modByMonicproof · cited by 82

Cited by1

Results whose statement or proof uses this declaration.

Polynomial.X_sub_C_dvd_derivative_of_X_sub_C_dvd_divByMonicproof · cited by 1