| import OAI.Combinatorics.LowSpaceSubsetSum.Streams.SliceCursor | |
| namespace OAI | |
| /-! # Attach one fixed first-array occurrence to a shared-array row reader -/ | |
| namespace LowSpaceSubsetSum | |
| namespace PairCursor | |
| variable {α β : Type*} | |
| structure State (α : Type*) (n : ℕ) where | |
| left : α | |
| cursor : SliceCursor.State n | |
| def next (xs : Array β) (s : State α xs.size) : Option ((α × β) × State α xs.size) := | |
| (SliceCursor.next xs s.cursor).map (fun z => ((s.left, z.1), ⟨s.left, z.2⟩)) | |
| def output (xs : Array β) (s : State α xs.size) : List (α × β) := | |
| (SliceCursor.output xs s.cursor).map (fun y => (s.left, y)) | |
| theorem reader (xs : Array β) : RowMerge.IsReader (next (α := α) xs) (output xs) := by | |
| intro s | |
| have hr := SliceCursor.reader xs s.cursor | |
| cases h : SliceCursor.next xs s.cursor with | |
| | none => | |
| simp only [h] at hr | |
| simp only [next, h, Option.map_none, output, hr, List.map_nil] | |
| | some z => | |
| obtain ⟨y, c⟩ := z | |
| simp only [h] at hr | |
| simp only [next, h, Option.map_some, output, hr, List.map_cons] | |
| end PairCursor | |
| end LowSpaceSubsetSum | |
| end OAI | |