Theorems · Theorem · commutative algebra
Polynomial.content_X_mul
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : NormalizedGCDMonoid R] {p : Polynomial R},
(Polynomial.X * p).content = p.content- Defined in
- Mathlib.RingTheory.Polynomial.Content
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 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.
Cites24
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
- Finsetproof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- mul_commproof · cited by 2,262
- Polynomial.Xstatement and proof · cited by 1,639
- MulZeroClass.zero_mulproof · cited by 1,625
- Polynomial.coeffproof · cited by 1,045
- Multiset.mapproof · cited by 876
- Finset.mapproof · cited by 747
- Finset.extproof · cited by 565
- Finset.valproof · cited by 438
- Polynomial.supportproof · cited by 237
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.content_X_powproof · cited by 1
- Polynomial.content_Xproof · cited by 0