Theorems · Theorem · field theory
Polynomial.Splits.dvd_of_roots_le_roots
∀ {R : Type u_1} [inst : Field R] {f g : Polynomial R}, f.Splits → f ≠ 0 → f.roots ≤ g.roots → f ∣ g- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement · cited by 2,627
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.rootsstatement and proof · cited by 264
- Dvd.dvd.transproof · cited by 148
- Polynomial.leadingCoeff_ne_zeroproof · cited by 39
- Polynomial.Splits.eq_prod_rootsproof · cited by 16
- Multiset.map_le_mapproof · cited by 14
- Multiset.prod_dvd_prod_of_leproof · cited by 9
- Polynomial.prod_multiset_X_sub_C_dvdproof · cited by 5
- Polynomial.C_mul_dvdproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Splits.dvd_iff_roots_le_rootsproof · cited by 1