Theorems · Theorem · ring theory
SkewPolynomial.monomial_mul_X_pow
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : MulSemiringAction (Multiplicative ℕ) R] (n : ℕ) (r : R) (k : ℕ),
(SkewPolynomial.monomial n) r * SkewPolynomial.X ^ k = (SkewPolynomial.monomial (n + k)) r- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- RingHom.idstatement · cited by 18,349
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- mul_oneproof · cited by 3,885
- add_zeroproof · cited by 2,707
- pow_zeroproof · cited by 1,094
- Multiplicativestatement and proof · cited by 875
- add_assocproof · cited by 746
- MulSemiringActionstatement and proof · cited by 423
- pow_succproof · cited by 374
- SkewPolynomialstatement · cited by 124
Cited by1
Results whose statement or proof uses this declaration.
- SkewPolynomial.X_pow_mul_monomialproof · cited by 0