[FRIAM] Diogenes, the Cynic ...

[glen]

Sorry. The unicode didn't come through the cut and paste ... stupid emacs.

Me: What does this formula mean: ∀v_i(v_i=v_1'⊃∀v_1(v_1=v_i⊃F)) ?

I'll try to do things more like them. E.g. "complete the following lean 4 code ..." instead of abusing it this way.

On 2/5/25 10:54 AM, glen wrote:
> 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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