Theorems · Theorem · field theory
Polynomial.isCoprime_X_sub_C_of_isUnit_sub
∀ {R : Type u_1} [inst : CommRing R] {a b : R},
IsUnit (a - b) → IsCoprime (Polynomial.X - Polynomial.C a) (Polynomial.X - Polynomial.C b)- Defined in
- Mathlib.Algebra.Polynomial.RingDivision
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 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.
Cites19
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
- RingHomstatement and proof · cited by 10,189
- Polynomialstatement and proof · cited by 5,681
- Units.valproof · cited by 1,966
- Polynomial.Xstatement and proof · cited by 1,639
- IsUnitstatement and proof · cited by 1,602
- Polynomial.Cstatement and proof · cited by 1,598
- DFunLikeproof · cited by 576
- IsCoprimestatement · cited by 321
- IsUnit.unitproof · cited by 252
- Polynomial.C_1proof · cited by 57
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.pairwise_coprime_X_sub_Cproof · cited by 3
- Polynomial.mul_star_dvd_of_aeval_eq_zero_im_ne_zeroproof · cited by 1