Theorems · Theorem · ring theory
SkewPolynomial.monomial_mul_X
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : MulSemiringAction (Multiplicative ℕ) R] (n : ℕ) (r : R),
(SkewPolynomial.monomial n) r * SkewPolynomial.X = (SkewPolynomial.monomial (n + 1)) r- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringMulSemiringAction
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- LinearMapstatement · cited by 10,215
- mul_oneproof · cited by 3,885
- Multiplicativestatement and proof · cited by 875
- MulSemiringActionstatement and proof · cited by 423
- SkewPolynomialstatement and proof · cited by 124
- SkewPolynomial.monomialstatement and proof · cited by 49
- SkewPolynomial.Xstatement · cited by 27
- SkewPolynomial.φproof · cited by 12
- SkewPolynomial.monomial_mul_monomialproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- SkewPolynomial.monomial_mul_X_powproof · cited by 1
- SkewPolynomial.X_mul_monomialproof · cited by 0