Theorems · Theorem · field theory
Polynomial.Splits.of_degree_le_one_of_invertible
∀ {R : Type u_1} [inst : Semiring R] {f : Polynomial R}, f.degree ≤ 1 → ∀ (h : Invertible f.leadingCoeff), f.Splits- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 1 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.
Cites9
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
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Invertiblestatement and proof · cited by 549
- Polynomial.leadingCoeffstatement and proof · cited by 498
- Polynomial.Splitsstatement · cited by 290
- Polynomial.natDegree_le_of_degree_leproof · cited by 16
- Polynomial.Splits.of_natDegree_le_one_of_invertibleproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.splits_of_degree_le_one_of_invertibleproof · cited by 0