Created
August 4, 2024 21:44
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| /- | |
| Written by user "-d" from the https://bbchallenge.org/ Discord (https://discord.gg/3uqtPJA9Uv) | |
| https://wiki.bbchallenge.org/wiki/BB(6) | |
| Hydra: | |
| https://wiki.bbchallenge.org/wiki/Hydra | |
| https://bbchallenge.org/1RB3RB---3LA1RA_2LA3RA4LB0LB0LA | |
| Antihydra: | |
| https://wiki.bbchallenge.org/wiki/Antihydra | |
| https://bbchallenge.org/1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA | |
| -/ | |
| import Init.Data.Nat.Basic | |
| import Mathlib.Data.Nat.Notation | |
| import Mathlib.Data.Int.Notation | |
| namespace bmo_p1 | |
| def f (ab : ℕ × ℕ) : ℕ × ℕ := | |
| let (a, b) := ab | |
| if a ≥ b then | |
| (a-b, 4*b+2) | |
| else | |
| (2*a+1, b-a) | |
| theorem bmo_p1_halt : ∃ i, (let (a, b) := Nat.repeat f i (1, 2); a = b) := by | |
| sorry | |
| theorem bmo_p1_nonhalt : ∀ i, (let (a, b) := Nat.repeat f i (1, 2); a ≠ b) := by | |
| sorry | |
| end bmo_p1 | |
| namespace bmo_antihydra | |
| def a (n : ℕ) : ℕ := match n with | |
| | 0 => 8 | |
| | n+1 => a n * 3 / 2 | |
| def b (n : ℕ) : ℤ := match n with | |
| | 0 => 0 | |
| | n+1 => b n + (if a n % 2 = 0 then 2 else -1) | |
| theorem bmo_antihydra_halt : ∃ k, b k < 0 := by | |
| sorry | |
| theorem bmo_antihydra_nonhalt : ∀ k, b k ≥ 0 := by | |
| sorry | |
| end bmo_antihydra |
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