Theorems · Theorem · ring theory
SkewPolynomial.X_mul
∀ {R : Type u_1} [inst : Semiring R] {p : SkewPolynomial R} [inst_1 : MulSemiringAction (Multiplicative ℕ) R],
SkewPolynomial.X * p = (p.sum fun a b => (SkewPolynomial.monomial a) (SkewPolynomial.φ b)) * SkewPolynomial.X- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 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.
Cites29
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
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- MulZeroClass.mul_zeroproof · cited by 2,091
- MulZeroClass.zero_mulproof · cited by 1,625
- map_zeroproof · cited by 1,614
- add_commproof · cited by 1,535
- map_addproof · cited by 964
Cited by2
Results whose statement or proof uses this declaration.
- SkewPolynomial.X_pow_mulproof · cited by 1
- SkewPolynomial.X_mul_monomialproof · cited by 0