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f18e7de | 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 | import OAI.MathematicalPhysics.AlternatingFlow.AnalyticResult
import OAI.MathematicalPhysics.AlternatingFlow.ForceNames
import OAI.MathematicalPhysics.AlternatingFlow.Compilers
namespace OAI
section MainResultDevelopment
namespace AlternatingNS
theorem alternating (ν : ℝ) (hν : 0 < ν) (hc : ComputableReal ν) :
AlternatingConclusion ν := by
obtain ⟨cf,hcf,hf⟩ := Effective.Certified.programs
(Effective.force_certified ν) (Effective.force_named ν hc)
obtain ⟨cu,hcu,hu⟩ := Effective.Certified.programs
Effective.velocity_certified Effective.velocity_named
refine ⟨cf,cu,hcf,hcu,Spatial.box,Spatial.box_compact,?_⟩
intro M w hM hw
obtain ⟨_,hfs,hUs,hfk,hUk,hfr,hUr,hr,hNS,hE,huniq,X,hX,hXuniq,hhalt⟩ :=
Construction.alternating_analytic ν hν M w hM hw
exact ⟨Construction.force ν M w,Construction.velocity M w,X,
(hf (M,w)).congr_half (Effective.fullForce_half ν M w),hu (M,w),
hfs,hUs,hfk,hUk,hfr,hUr,hr,hNS,hE,huniq,hX,hXuniq,hhalt⟩
end AlternatingNS
end MainResultDevelopment
end OAI
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