Theorems · Theorem · field theory
Polynomial.eq_zero_of_dvd_of_natDegree_lt
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] {p q : Polynomial R}, p ∣ q → q.natDegree < p.natDegree → q = 0- Defined in
- Mathlib.Algebra.Polynomial.Degree.Domain
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 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.
Cites6
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
- NoZeroDivisorsstatement and proof · cited by 545
- lt_iff_not_geproof · cited by 22
- Polynomial.natDegree_le_of_dvdproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.not_dvd_of_natDegree_ltproof · cited by 0