starMap_comp — Mathlib

English

StarMap respects composition: starMap(ψ ∘ φ) = (starMap ψ) ∘ (starMap φ).

Русский

StarMap сохраняет композицию: starMap(ψ ∘ φ) = (starMap ψ) ∘ (starMap φ).

LaTeX

$$$\mathrm{starMap}(\psi\circ\phi)=(\mathrm{starMap}\psi)\circ (\mathrm{starMap}\phi).$$$

Lean4

/-- `starMap` is functorial: `starMap (ψ.comp φ) = (starMap ψ).comp (starMap φ)`. -/
theorem starMap_comp {φ : A →⋆ₙₐ[R] B} {ψ : B →⋆ₙₐ[R] C} : starMap (ψ.comp φ) = (starMap ψ).comp (starMap φ) := by ext;
  all_goals simp

Похожие утверждения