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lengyijun committed Oct 14, 2024
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8 changes: 4 additions & 4 deletions GoldbachTm/Tm31/Content.lean
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import GoldbachTm.Tm31.TuringMachine31
import Mathlib.Data.Nat.Prime.Defs

theorem lemma_25 (k : ℕ): ∀ (i : ℕ),
nth_cfg i = some ⟨⟨25, by omega⟩, ⟨Γ.zero, Turing.ListBlank.mk (List.replicate k Γ.one), Turing.ListBlank.mk []⟩⟩ →
(¬ (∃ x y, x + y = k /\ Nat.Prime x /\ Nat.Prime y)) →
∃ j, nth_cfg (i+j) = some ⟨⟨25, by omega⟩, ⟨Γ.zero, Turing.ListBlank.mk (List.replicate (k+2) Γ.one), Turing.ListBlank.mk []⟩⟩
theorem lemma_25 (n : ℕ): ∀ (i : ℕ),
nth_cfg i = some ⟨⟨25, by omega⟩, ⟨Γ.zero, Turing.ListBlank.mk (List.replicate n Γ.one), Turing.ListBlank.mk []⟩⟩ →
(∃ x y, x + y = n /\ Nat.Prime x /\ Nat.Prime y) →
∃ j, nth_cfg (i+j) = some ⟨⟨25, by omega⟩, ⟨Γ.zero, Turing.ListBlank.mk (List.replicate (n+2) Γ.one), Turing.ListBlank.mk []⟩⟩
:= by
sorry

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