Theorems · Theorem · field theory
Polynomial.Splits.of_natDegree_le_one
∀ {R : Type u_1} [inst : DivisionSemiring R] {f : Polynomial R}, f.natDegree ≤ 1 → f.Splits- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Polynomialstatement and proof · cited by 5,681
- zero_addproof · cited by 2,366
- 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
- mul_addproof · cited by 413
- Polynomial.Splitsstatement and proof · cited by 290
- DivisionSemiringstatement and proof · cited by 216
- mul_inv_cancel_left₀proof · cited by 42
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.Splits.of_degree_le_oneproof · cited by 2
- Polynomial.Splits.of_natDegree_eq_oneproof · cited by 1
- perfectField_iff_splits_of_natSepDegree_eq_oneproof · cited by 1
- Polynomial.Gal.splits_in_splittingField_of_compproof · cited by 1