Theorems · Theorem · field theory
Polynomial.isUnit_of_self_mul_dvd_separable
∀ {R : Type u} [inst : CommSemiring R] {p q : Polynomial R}, p.Separable → q * q ∣ p → IsUnit q- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.coeproof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- IsUnitstatement · cited by 1,602
- mul_addproof · cited by 413
- Polynomial.derivativeproof · cited by 331
- IsCoprimeproof · cited by 321
- Polynomial.Separablestatement and proof · cited by 117
- Polynomial.derivative_mulproof · cited by 35
- IsCoprime.of_mul_left_leftproof · cited by 8
- IsCoprime.of_mul_right_leftproof · cited by 4
- isCoprime_selfproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.emultiplicity_le_one_of_separableproof · cited by 3
- Polynomial.nodup_of_separable_prodproof · cited by 1