simp
case a
a b : String
n : ℕ
⊢ Ø ⋁ (∀ₛ b ; _ a +ₛ _ b =ₛ _ b +ₛ _ a) [a ≔ fromNat n]
case a
a b : String
n : ℕ
⊢ Ø ⋁
    match String.decEq a b with
    | isTrue h => ∀ₛ b ; _ a +ₛ _ b =ₛ _ b +ₛ _ a
    | isFalse h =>
      ∀ₛ b ;
        ((match String.decEq a a with
            | isTrue h => fromNat n
            | isFalse h => _ a) +ₛ
            match String.decEq a b with
            | isTrue h => fromNat n
            | isFalse h => _ b) =ₛ
          (match String.decEq a b with
            | isTrue h => fromNat n
            | isFalse h => _ b) +ₛ
            match String.decEq a a with
            | isTrue h => fromNat n
            | isFalse h => _ a