| import Mathlib | |
| import OAI.Computability.VertexCover.Machines.Primitives | |
| namespace OAI | |
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| namespace VertexCover.Machine | |
| theorem prodBits_injective {α β : Type} {ea : α → List Bool} {eb : β → List Bool} | |
| (ha : Function.Injective ea) (hb : Function.Injective eb) : | |
| Function.Injective (prodBits ea eb) := by | |
| intro a b h | |
| apply Prod.ext | |
| · apply ha | |
| have hh := congrArg (Stream.output (Project.trans true false) (fun _ => []) 0) h | |
| simpa only [prodBits,Project.framed,Bool.false_eq_true,↓reduceIte,List.append_nil] using hh | |
| · apply hb | |
| have hh := congrArg (Stream.output (Project.trans false true) (fun _ => []) 0) h | |
| simpa only [prodBits,Project.framed,Bool.false_eq_true,↓reduceIte,List.nil_append] using hh | |
| theorem boolBits_injective : Function.Injective boolBits := by | |
| intro a b h | |
| exact List.singleton_injective h | |
| end VertexCover.Machine | |
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| end OAI | |