Theorems · Theorem · commutative algebra
Polynomial.degree_gcd_le_right
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] (p : Polynomial R) {q : Polynomial R},
q ≠ 0 → (gcd p q).degree ≤ q.degree- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingNormalizedGCDMonoid
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Cites8
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 · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- NormalizedGCDMonoidstatement and proof · cited by 159
- GCDMonoid.gcdstatement · cited by 143
- gcd_commproof · cited by 6
- Polynomial.degree_gcd_le_leftproof · cited by 1
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