dsimp
case zero
a b c : ℤθ
⊢ ∃ a b c,
    { f := -23, g := -63, h := -15 }.f = 1 + 3 + 3 ^ 2 * a ∧
      { f := -23, g := -63, h := -15 }.g = 3 ^ 2 * b ∧ { f := -23, g := -63, h := -15 }.h = 3 + 3 ^ 2 * c
case zero
a b c : ℤθ
⊢ ∃ a b c, -23 = 1 + 3 + 3 ^ 2 * a ∧ -63 = 3 ^ 2 * b ∧ -15 = 3 + 3 ^ 2 * c