comp — Mathlib

English

init_n is compatible with natural scalar multiplication: init_n(m • x) = m • init_n(x).

Русский

init_n совместимо с натуральным скаляром: init_n(m · x) = m · init_n(x).

LaTeX

$$$$\operatorname{init}_n(m \cdot x) = m \cdot \operatorname{init}_n x.$$$$

Lean4

/-- The composition of polynomial functions is polynomial. -/
instance comp {g f} [hg : IsPoly p g] [hf : IsPoly p f] : IsPoly p fun R _Rcr => @g R _Rcr ∘ @f R _Rcr :=
  by
  obtain ⟨φ, hf⟩ := hf
  obtain ⟨ψ, hg⟩ := hg
  use fun n => bind₁ φ (ψ n)
  intros
  simp only [aeval_bind₁, Function.comp, hg, hf]

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