| import Mathlib | |
| import OAI.MathematicalPhysics.RecorderFlows.Effective | |
| namespace OAI | |
| /-! The initialized solenoidal-flow conclusion as a mathematical specification. -/ | |
| namespace Solenoidal | |
| def Initialized : Prop := | |
| ∃ (U : (M : Machine) → List M.Symbol → Fluid.Field) (V : Machine → Fluid.Field) | |
| (eval bounds : Effective.OracleCode), | |
| (∀ (M : Machine) (w : List M.Symbol) (p : Fluid.SpaceTime), | |
| 1 ≤ p 0 → U M w p = V M (Fluid.translateTime (-1) p)) ∧ | |
| Effective.RelativeEffective (fun ν M w => Fluid.force ν (U M w)) eval bounds ∧ | |
| (∀ ν : ℝ, 0 < ν → Effective.ComputableReal ν → | |
| Effective.EffectiveAt (fun μ M w => Fluid.force μ (U M w)) ν) ∧ | |
| (∀ ν : ℝ, 0 < ν → ∀ (M : Machine) (w : List M.Symbol), | |
| Fluid.FluidAssertions ν (U M w) (Fluid.force ν (U M w)) ∧ | |
| Fluid.BoundedPeriodicAssertions (U M w) (Fluid.force ν (U M w)) ∧ | |
| Fluid.ObservationAssertion M w (U M w)) ∧ | |
| (∀ ν : ℝ, 0 < ν → ∀ (M : Machine) (w w' : List M.Symbol) (p : Fluid.SpaceTime), | |
| 1 ≤ p 0 → Fluid.force ν (U M w) p = Fluid.force ν (U M w') p) | |
| end Solenoidal | |
| end OAI | |