Theorems · Theorem · field theory
Polynomial.not_dvd_of_natDegree_lt
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] {p q : Polynomial R}, q ≠ 0 → q.natDegree < p.natDegree → ¬p ∣ q- Defined in
- Mathlib.Algebra.Polynomial.Degree.Domain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
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Cites5
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
- Polynomial.eq_zero_of_dvd_of_natDegree_ltproof · cited by 1
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