Theorems · Theorem · field theory
Polynomial.degree_pos_of_not_isUnit_of_dvd_monic
∀ {R : Type u} [inst : CommSemiring R] {a p : Polynomial R}, p.Monic → ¬IsUnit a → a ∣ p → 0 < a.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Units
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- IsUnitstatement and proof · cited by 1,602
- WithBotstatement · cited by 1,498
- Polynomial.coeffproof · cited by 1,045
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.eq_C_of_degree_le_zeroproof · cited by 20
- Polynomial.Monic.C_dvd_iff_isUnitproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Monic.irreducible_iff_degree_ltproof · cited by 1
- Polynomial.natDegree_pos_of_not_isUnit_of_dvd_monicproof · cited by 0