Theorems · Theorem · field theory
Polynomial.Splits.of_natDegree_le_one_of_invertible
∀ {R : Type u_1} [inst : Semiring R] {f : Polynomial R}, f.natDegree ≤ 1 → ∀ (h : Invertible f.leadingCoeff), 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
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- add_zeroproof · cited by 2,707
- 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
- eq_or_neproof · cited by 1,117
- Polynomial.natDegreestatement and proof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.Splits.comp_of_natDegree_le_one_of_invertibleproof · cited by 3
- Polynomial.Splits.of_natDegree_le_one_of_monicproof · cited by 2
- Polynomial.Splits.of_degree_le_one_of_invertibleproof · cited by 1
- Polynomial.splits_of_natDegree_le_one_of_invertibleproof · cited by 0