Theorems · Theorem · commutative algebra
Polynomial.degree_gcd_le_left
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] {p : Polynomial R},
p ≠ 0 → ∀ (q : Polynomial R), (gcd p q).degree ≤ p.degree- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNormalizedGCDMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.degreestatement and proof · cited by 643
- NormalizedGCDMonoidstatement and proof · cited by 159
- GCDMonoid.gcdstatement and proof · cited by 143
- Polynomial.degree_eq_natDegreeproof · cited by 69
- GCDMonoid.gcd_dvd_leftproof · cited by 36
- Polynomial.natDegree_le_iff_degree_leproof · cited by 12
- Polynomial.natDegree_le_of_dvdproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.degree_gcd_le_rightproof · cited by 0