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