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caec230 | 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 | import Mathlib
import OAI.MathematicalPhysics.RecorderFlows.Model
import OAI.Computability.SolenoidalRecorder.Machines
namespace OAI
/-! Fixed-label material trajectories and the machine observation specification. -/
namespace Solenoidal
namespace Fluid
noncomputable def label : Space := ![1 / 8, 3 / 8, 1 / 2]
def InStrip (x : Space) : Prop := (1 / 2 : ℝ) < Int.fract (x 0) ∧ Int.fract (x 0) < 1
def Trajectory (U : Field) (X : ℝ → Space) : Prop :=
X 0 = label ∧ ∀ t : ℝ, 0 ≤ t →
HasDerivWithinAt X (U (point t (X t))) (Set.Ici 0) t
def ObservationAssertion (M : Machine) (w : List M.Symbol) (U : Field) : Prop :=
∃ X : ℝ → Space, Trajectory U X ∧
(∀ Y : ℝ → Space, Trajectory U Y → ∀ t : ℝ, 0 ≤ t → Y t = X t) ∧
((∃ t : ℝ, 0 ≤ t ∧ InStrip (X t)) ↔ M.Halts w)
end Fluid
end Solenoidal
end OAI
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