feat: add helper List.append simp theorems

src/Init/Data/List/BasicAux.lean

@@ -121,4 +121,28 @@ theorem sizeOf_lt_of_mem [SizeOf α] {as : List α} (h : a ∈ as) : sizeOf a <
   | head => simp_arith
   | tail _ _ ih => exact Nat.lt_trans ih (by simp_arith)
 
+theorem append_cancel_left {as bs cs : List α} (h : as ++ bs = as ++ cs) : bs = cs := by
+  induction as with
+  | nil => assumption
+  | cons a as ih =>
+    injection h with _ h
+    exact ih h
+
+theorem append_cancel_right {as bs cs : List α} (h : as ++ bs = cs ++ bs) : as = cs := by
+  match as, cs with
+  | [], []       => rfl
+  | [], c::cs    => have aux := congrArg length h; simp_arith at aux
+  | a::as, []    => have aux := congrArg length h; simp_arith at aux
+  | a::as, c::cs => injection h with h₁ h₂; subst h₁; rw [append_cancel_right h₂]
+
+@[simp] theorem append_cancel_left_eq (as bs cs : List α) : (as ++ bs = as ++ cs) = (bs = cs) := by
+  apply propext; apply Iff.intro
+  next => apply append_cancel_left
+  next => intro h; simp [h]
+
+@[simp] theorem append_cancel_right_eq (as bs cs : List α) : (as ++ bs = cs ++ bs) = (as = cs) := by
+  apply propext; apply Iff.intro
+  next => apply append_cancel_right
+  next => intro h; simp [h]
+
 end List