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e5a97c6 | 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 40 41 42 43 44 45 46 47 48 | import Mathlib
import OAI.Combinatorics.MatchingCount.Algorithm.OnlineRequest
import OAI.Combinatorics.MatchingCount.Algorithm.OnlineTransitionLaw
namespace OAI
namespace MatchingFPRAS.OnlineSchedule
open PhysicalStream TreeTyped TreeFraction ExecutableSource ExecutableScaling Transport
open UnitRefresh Enlargement TreeTyped.Numbered OnlineStage ExecutableRefresh
attribute [local instance] NumberedHierarchy.labelOrder
attribute [local instance] Transport.sym2Order Transport.bagEdgeOrder Transport.bagEdgeFintype
attribute [local instance] UnitRefresh.Computable.allowedDec Transport.prodOrder Transport.sumOrder
lemma bitPrecision_inverseNat (R m : ℕ) : bitPrecision R (1/(m:ℚ))=Nat.clog 2 (R*m) := by
simp [bitPrecision]
variable {G : GraphInput} [Nontrivial (Fin G.n)]
lemma sourceRequest_source {j : ℕ} (p : Trial.Parameters G) (s : FiniteTrial.ScaleState G j) :
sourceRequest (fixedData p s,p.S)=fixedRequest p s := by
unfold sourceRequest
rw [show sourcePrecision (fixedData p s,p.S)=
(((((Fintype.card (SourceVertex (Fin G.n) p.K)),FiniteTrial.sourceD (G:=G) p.K),
(p.K,tierCount (n:=G.n) p.K (FiniteTrial.sourceD (G:=G) p.K))),denominator p),
(edgeCount s.activity p.K,labelCount s.activity p.K)) from by
simpa only [fixedData,denominator,edgeCount,labelCount,List.length_replicate] using
sourcePrecision_source p.hn s p.K (FiniteTrial.sourceD (G:=G) p.K) p.S
(List.replicate (tierCount (n:=G.n) p.K (FiniteTrial.sourceD (G:=G) p.K)) false)
(List.replicate (copies (n:=G.n) p.K (FiniteTrial.sourceD (G:=G) p.K)) false)]
have hc : (sourceTables (sparseBagInput (fixedData p s))).1.length=edgeCount s.activity p.K := by
unfold fixedData
rw [sparseBagInput_source,sourceTables_catalog p.hn s.activity
(fun i j=>(s.activity_pos i j).le) p.K]
simp only [sourceCatalog,List.length_ofFn]
simp only [hc,precisionPlan,fixedRequest,choiceWidth,markWidth,bitPrecision_inverseNat]
apply Prod.ext
· rfl
· apply Prod.ext
· rfl
· simp only [index_orderedEnum]
apply List.ext_getElem
· simp
· intro _ _ _
simp
end MatchingFPRAS.OnlineSchedule
end OAI
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