Theorems · Theorem · field theory
Polynomial.IsRoot.dvd_coeff_zero
∀ {R : Type u} [inst : CommRing R] {p : Polynomial R} {x : R}, p.IsRoot x → x ∣ p.coeff 0- Defined in
- Mathlib.Algebra.Polynomial.Div
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
- sub_zeroproof · cited by 938
- Polynomial.evalproof · cited by 796
- zero_subproof · cited by 335
- Polynomial.IsRootstatement and proof · cited by 152
- Polynomial.coeff_zero_eq_eval_zeroproof · cited by 20
- Polynomial.IsRoot.eq_zeroproof · cited by 3
- Polynomial.sub_dvd_eval_subproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsIntegral.coeffproof · cited by 4