Theorems · Theorem · field theory
Polynomial.Splits.of_natDegree_le_one_of_monic
∀ {R : Type u_1} [inst : Semiring R] {f : Polynomial R}, f.natDegree ≤ 1 → f.Monic → f.Splits- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.Splitsstatement · cited by 290
- Polynomial.Monic.leadingCoeffproof · cited by 101
- invertibleOneproof · cited by 8
- Polynomial.Splits.of_natDegree_le_one_of_invertibleproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Splits.of_degree_le_one_of_monicproof · cited by 1
- Polynomial.splits_of_natDegree_le_one_of_monicproof · cited by 0