Theorems · Theorem · field theory
Polynomial.X_sub_C_dvd_derivative_of_X_sub_C_dvd_divByMonic
∀ {K : Type u_1} [inst : Field K] (f : Polynomial K) {a : K},
Polynomial.X - Polynomial.C a ∣ f /ₘ (Polynomial.X - Polynomial.C a) →
Polynomial.X - Polynomial.C a ∣ Polynomial.derivative f- Defined in
- Mathlib.Algebra.Polynomial.FieldDivision
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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
- LinearMapstatement · cited by 10,215
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- mul_addproof · cited by 413
- Polynomial.derivativestatement and proof · cited by 331
- Polynomial.divByMonicstatement and proof · cited by 77
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.isCoprime_of_is_root_of_eval_derivative_ne_zeroproof · cited by 0