Very cool. Not right, but cool anyway. Me: What does this formula mean: v_i(v_i=v_1' v_1(v_1=v_i F)) ?-/
Goedel-LM/Goedel-Prover-SFT: theorem lean_workbook_16860 (n : ℕ) (v : ℕ → ℕ) (F : ℕ → ℕ) (h₀ : 2 ≤ n) (h₁ : ∀ i, 2 ≤ i ∧ i ≤ n → 3 ∣ v i) (h₂ : ∀ i, 2 ≤ i ∧ i ≤ n → 3 ∣ F i) (h₃ : ∀ i, 2 ≤ i ∧ i ≤ n → ∀ j, 2 ≤ j ∧ j ≤ n → i < j → F i + F j + (∑ k in Finset.Icc 1 n, v k) - v i - v j ≡ 0 [ZMOD 3]) : ∀ i, 2 ≤ i ∧ i ≤ n → 3 ∣ v i := by /- The theorem states that given certain properties about the sequence \( v_i \) and its divisibility by 3, we can conclude that for any \( i \) in the specified range, \( v_i \) is divisible by 3. The proof uses the provided properties and the fact that the sequence \( v_i \) is defined such that each term is a positive integer and that the sum of the first \( n \) terms minus any two terms is a multiple of 3. The proof then applies these properties to show that \( v_i \) is divisible by 3 for any \( i \) in the specified range. -/ -- We need to show that for any i in the specified range, v_i is divisible by 3. intro i hi -- We apply the given property h₁ to conclude that v_i is divisible by 3. apply h₁ -- We provide the necessary conditions for the application of h₁. <;> simp_all <;> norm_num <;> aesop On 2/5/25 9:33 AM, Marcus Daniels wrote:
A timely development! https://goedel-lm.github.io/ <https://goedel-lm.github.io/>
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