∀ (a : ℤ) {b : ℤ} (motive : (∃ z, 0 ≤ z ∧ z < b ∧ z ≡ a [ZMOD b]) → Prop) (x : ∃ z, 0 ≤ z ∧ z < b ∧ z ≡ a [ZMOD b]),
  (∀ (z : ℤ) (hz1 : 0 ≤ z) (hz2 : z < b) (hz3 : z ≡ a [ZMOD b]), motive ⋯) → motive x