Theorems · Theorem · field theory
Polynomial.splits_iff_comp_splits_of_natDegree_eq_one
∀ {R : Type u_1} [inst : Field R] {f g : Polynomial R}, g.natDegree = 1 → (f.Splits ↔ (f.comp g).Splits)- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 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.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- one_mulproof · cited by 2,841
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
- mul_assocproof · cited by 1,667
- Polynomial.Xproof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- Polynomial.Cproof · cited by 1,598
- Polynomial.natDegreestatement and proof · cited by 1,105
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.splits_iff_comp_splits_of_degree_eq_oneproof · cited by 0