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/>
--
¡sıɹƎ ןıɐH ⊥ ɐןןǝdoɹ ǝ uǝןƃ
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