Theorems · Theorem · field theory
Polynomial.not_isUnit_of_degree_pos
∀ {R : Type u} [inst : Semiring R] [NoZeroDivisors R] (p : Polynomial R), 0 < p.degree → ¬IsUnit p- Defined in
- Mathlib.Algebra.Polynomial.Degree.Units
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 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.
Cites9
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
- Nontrivialproof · cited by 2,416
- IsUnitstatement and proof · cited by 1,602
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- NoZeroDivisorsstatement and proof · cited by 545
- subsingleton_or_nontrivialproof · cited by 161
- Polynomial.degree_eq_zero_of_isUnitproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.not_isUnit_of_natDegree_posproof · cited by 5