Theorems · Theorem · ring theory
SkewPolynomial.coeff_update_apply
Deprecated since 2026-07-06Use SkewPolynomial.coeff_update instead.
∀ {R : Type u_1} [inst : Semiring R] (p : SkewPolynomial R) (n : ℕ) (a : R) (i : ℕ),
(p.update n a).coeff i = if i = n then a else p.coeff i- Defined in
- Mathlib.Algebra.SkewPolynomial.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Multiplicative.ofAddproof · cited by 237
- SkewPolynomialstatement and proof · cited by 124
- SkewPolynomial.coeffstatement · cited by 37
- SkewPolynomial.updatestatement · cited by 9
- SkewMonoidAlgebra.coeff_update_applyproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- SkewPolynomial.coeff_update_neproof · cited by 0
- SkewPolynomial.coeff_update_sameproof · cited by 0