| import OAI.Computability.SpaceSimulation.Evaluation.Evaluate |
| import OAI.Computability.SpaceSimulation.Epoch.Uniform |
| import OAI.Computability.SpaceSimulation.Epoch.Agrees |
| import OAI.Computability.SpaceSimulation.Epoch.Meter |
|
|
| namespace OAI |
|
|
| namespace Fifths.Tour |
|
|
| def visits (D : Tour) := D.E * D.b |
|
|
| theorem finalDigit (D : Tour) (g : D.FiniteWords) : |
| Radix.get D.m (D.valueOf D.target) D.b = (D.story D.visits).ctrl := by |
| unfold target |
| rw [D.at_history (by unfold E; omega) le_rfl] |
| have e := D.log_agrees g ((D.E-1)*D.b) D.b D.b le_rfl |
| simpa [visits,E,add_mul,b] using e |
|
|
| attribute [local irreducible] Fifths.Bin.pair Fifths.Modulus.chosen |
|
|
| /-- Epoch application. No simulation-specific assumptions beyond |
| bounded words, uniform interface, and appropriate amount of space. -/ |
| theorem follows {I X : Type} {D : I → Tour} {x : I → List X} {S cp} |
| (q : Runnable D x S cp) (g : ∀ i, (D i).FiniteWords) |
| (h : Scaled S (fun i => (D i).E * (D i).per)) : |
| Comp x S cp (fun i => ((D i).story (D i).visits).ctrl) := by |
| let C := fun i => (D i).circuit |
| have b : Comp x S cp (fun i => (D i).target.val) := |
| q.makeV (r := id) (Comp.refl q.kOf.source) q.kOf.plus1.minus1 (q.nOf.add q.kOf) |
| have l := Circuit.evaluate (q.ready g) (fun i => (D i).certified (g i)) |
| (fun i => (D i).coins) (fun i => (D i).covers) (fun i => (D i).target) |
| b (h.of_le (fun i => (D i).coins_total _)) |
| have y := Comp.digit q.mOf l q.bOf (q.powersFit id (fun i => Nat.le_succ (D i).b)) |
| exact y.congr (fun i => (D i).finalDigit (g i)) |
|
|
| end Fifths.Tour |
|
|
| end OAI |
|
|
