| 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 |
|
|
