∀ {α : Type u} {β : Type v} {x : BEq α} {x_1 : Hashable α} {m : Std.HashMap α β} [EquivBEq α] [LawfulHashable α]
  [inst : Inhabited β] {l : List (α × β)} {k : α},
  (List.map Prod.fst l).contains k = false → (m.insertMany l)[k]! = m[k]!