intros
case map_add
K : Type
inst✝⁷ : RCLike K
Cont : Type
Idx Elem : outParam Type
inst✝⁶ : ArrayType Cont Idx Elem
inst✝⁵ : IndexType Idx
inst✝⁴ : LawfulIndexType Idx
inst✝³ : DecidableEq Idx
R : Type
inst✝² : CommSemiring R
inst✝¹ : AddCommGroup Elem
inst✝ : Module R Elem
idx : Idx
⊢ ∀ (x y : Cont × Elem),
    (match x + y with
      | (cont, elem) => set cont idx elem) =
      (match x with
        | (cont, elem) => set cont idx elem) +
        match y with
        | (cont, elem) => set cont idx elem
case map_add
K : Type
inst✝⁷ : RCLike K
Cont : Type
Idx Elem : outParam Type
inst✝⁶ : ArrayType Cont Idx Elem
inst✝⁵ : IndexType Idx
inst✝⁴ : LawfulIndexType Idx
inst✝³ : DecidableEq Idx
R : Type
inst✝² : CommSemiring R
inst✝¹ : AddCommGroup Elem
inst✝ : Module R Elem
idx : Idx
x✝ y✝ : Cont × Elem
⊢ (match x✝ + y✝ with
    | (cont, elem) => set cont idx elem) =
    (match x✝ with
      | (cont, elem) => set cont idx elem) +
      match y✝ with
      | (cont, elem) => set cont idx elem