All-Russian Regional Preparation NT Exercise 4

Does there exist a geometric progression of $5$ two-digit natural numbers?

Replace sorry in the template below with your solution. See Answer Bank for acceptible answer declarations. Mathlib version used by the checker is v4.34.0.

import Mathlib.Data.Real.Basic

def answer : Prop := sorry

theorem solution : (∃ a₁ a₂ a₃ a₄ a₅ : ℕ,
    10 ≤ a₁ ∧ a₁ < a₂ ∧ a₂ < a₃ ∧ a₃ < a₄ ∧ a₄ < a₅ ∧ a₅ < 100 ∧
    ∃ d : ℝ, d * a₁ = a₂ ∧ d * a₂ = a₃ ∧ d * a₃ = a₄ ∧ d * a₄ = a₅) ↔ answer := sorry

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