Theorems · Theorem · field theory
Polynomial.Separable.mul
∀ {R : Type u} [inst : CommRing R] {f g : Polynomial R}, f.Separable → g.Separable → IsCoprime f g → (f * g).Separable- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- Polynomial.derivativeproof · cited by 331
- IsCoprimestatement and proof · cited by 321
- Polynomial.Separablestatement and proof · cited by 117
- Polynomial.derivative_mulproof · cited by 35
- IsCoprime.symmproof · cited by 22
- Polynomial.separable_defproof · cited by 7
- IsCoprime.mul_leftproof · cited by 6
- IsCoprime.add_mul_left_rightproof · cited by 4
- IsCoprime.mul_add_right_rightproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.separable_prod'proof · cited by 2