English
Appending a concrete list to a ListBlank constructed from another list equals constructing a ListBlank from the concatenation: ListBlank.append l1 (ListBlank.mk l2) = ListBlank.mk (l1 ++ l2).
Русский
Склейка списка l1 с ListBlank, построенным из l2, равна构造ному ListBlank из конкатенации: ListBlank.append l1 (ListBlank.mk l2) = ListBlank.mk (l1 ++ l2).
LaTeX
$$$\forall {\Gamma} [Inhabited(\Gamma)] (l_1 l_2 : List(\Gamma)), ListBlank.append l_1 (ListBlank.mk l_2) = ListBlank.mk (l_1 ++ l_2)$$$
Lean4
@[simp]
theorem append_mk {Γ} [Inhabited Γ] (l₁ l₂ : List Γ) :
ListBlank.append l₁ (ListBlank.mk l₂) = ListBlank.mk (l₁ ++ l₂) := by
induction l₁ <;> simp only [*, ListBlank.append, List.nil_append, List.cons_append, ListBlank.cons_mk]
