Theorems · Theorem · ring theory
SkewPolynomial.monomial_mul_monomial
∀ {R : Type u_1} [inst : Semiring R] [inst_1 : MulSemiringAction (Multiplicative ℕ) R] (n m : ℕ) (r s : R),
(SkewPolynomial.monomial n) r * (SkewPolynomial.monomial m) s =
(SkewPolynomial.monomial (n + m)) (r * (⇑SkewPolynomial.φ)^[n] s)- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 76 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.
Cites13
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
- RingHomstatement · cited by 10,189
- Multiplicativestatement and proof · cited by 875
- Nat.iteratestatement · cited by 740
- MulSemiringActionstatement and proof · cited by 423
- SkewPolynomialstatement · cited by 124
- SkewPolynomial.monomialstatement and proof · cited by 49
- SkewPolynomial.φstatement · cited by 12
- SkewMonoidAlgebra.single_mul_singleproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- SkewPolynomial.X_pow_eq_monomialproof · cited by 2
- SkewPolynomial.monomial_mul_Xproof · cited by 2
- SkewPolynomial.monomial_one_right_eq_X_powproof · cited by 0
- SkewPolynomial.monomial_mul_Cproof · cited by 0
- SkewPolynomial.C_mul_monomialproof · cited by 0