comp_assoc — Mathlib

English

Composition of partial functions is associative: (f.comp g).comp h = f.comp (g.comp h).

Русский

Композиция частичных функций ассоциативна: (f.comp g).comp h = f.comp (g.comp h).

LaTeX

$$$$ (f.comp g).comp h = f.comp (g.comp h). $$$$

Lean4

@[simp]
theorem comp_assoc (f : γ →. δ) (g : β →. γ) (h : α →. β) : (f.comp g).comp h = f.comp (g.comp h) :=
  ext fun _ _ => by
    simp only [comp_apply, Part.bind_comp]
      -- This can't be `simp`

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