Theorems · Theorem · field theory
Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C
∀ {R : Type u} [inst : CommRing R] {n : ℕ} (a b c : R),
↑n = 0 → IsUnit b → (Polynomial.C a * Polynomial.X ^ n + Polynomial.C b * Polynomial.X + Polynomial.C c).SeparableIf n = 0 in R and b is a unit, then a * X ^ n + b * X + c is separable.
- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 110 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.
Cites29
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
- CommRingstatement and proof · cited by 17,173
- Semiringproof · cited by 13,802
- RingHomstatement · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Polynomial.Xstatement and proof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
Cited by2
Results whose statement or proof uses this declaration.
- IsSepClosed.exists_root_C_mul_X_pow_add_C_mul_X_add_Cproof · cited by 1
- Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C'proof · cited by 0