Theorems · Theorem · ring theory
SkewPolynomial.X_pow_eq_monomial
∀ {R : Type u_1} [inst : Semiring R] (n : ℕ) [inst_1 : MulSemiringAction (Multiplicative ℕ) R],
SkewPolynomial.X ^ n = (SkewPolynomial.monomial n) 1- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 85 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.
Cites21
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
- add_commproof · cited by 1,535
- pow_zeroproof · cited by 1,094
- Multiplicativestatement and proof · cited by 875
- map_oneproof · cited by 861
- MulSemiringActionstatement and proof · cited by 423
- Multiplicative.ofAddproof · cited by 237
- pow_succ'proof · cited by 228
Cited by2
Results whose statement or proof uses this declaration.
- SkewPolynomial.support_X_powproof · cited by 1
- SkewPolynomial.smul_X_eq_monomialproof · cited by 0