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472a116 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | 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
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