Theorems · Theorem · field theory
Polynomial.degree_le_of_dvd
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] {p q : Polynomial R}, p ∣ q → q ≠ 0 → p.degree ≤ q.degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Domain
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 643
- NoZeroDivisorsstatement and proof · cited by 545
- mul_ne_zero_iffproof · cited by 39
- Polynomial.degree_le_mul_leftproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.eq_zero_of_dvd_of_degree_ltproof · cited by 3
- AdjoinRoot.of.injective_of_degree_ne_zeroproof · cited by 1
- Polynomial.degree_annIdealGenerator_le_of_memproof · cited by 1
- irreducible_X_pow_sub_C_of_root_adjoin_eq_topproof · cited by 1
- degree_radical_leproof · cited by 0