Theorems · Theorem · ring theory
SkewPolynomial.X_pow_mul_monomial
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : MulSemiringAction (Multiplicative ℕ) R] (k n : ℕ) (r : R),
SkewPolynomial.X ^ k * (SkewPolynomial.monomial n) r = (SkewPolynomial.monomial (n + k)) ((⇑SkewPolynomial.φ)^[k] r)- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringMulSemiringAction
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Cites17
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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- map_zeroproof · cited by 1,614
- Multiplicativestatement and proof · cited by 875
- Nat.iteratestatement and proof · cited by 740
- MulSemiringActionstatement and proof · cited by 423
- SkewPolynomialstatement · cited by 124
- SkewPolynomial.monomialstatement and proof · cited by 49
- SkewPolynomial.Xstatement and proof · cited by 27
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