comp₂ — Mathlib

English

init distributes over power: init_n(x^m) = init_n(x)^m within the Witt structure.

Русский

init распространяется на степень: init_n(x^m) = init_n(x)^m в Witt-структуре.

LaTeX

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

Lean4

/-- The composition of a polynomial function with a binary polynomial function is polynomial. -/
instance comp₂ {g f} [hg : IsPoly p g] [hf : IsPoly₂ p f] : IsPoly₂ p fun _ _Rcr x y => g (f x y) :=
  by
  obtain ⟨φ, hf⟩ := hf
  obtain ⟨ψ, hg⟩ := hg
  use fun n => bind₁ φ (ψ n)
  intros
  simp only [peval, aeval_bind₁, hg, hf]

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