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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 | import Mathlib
import OAI.Combinatorics.MatchingCount.Sampling.Sewn
import OAI.Combinatorics.MatchingCount.Sampling.FiniteSampler
import OAI.Combinatorics.MatchingCount.Sampling.FiniteSampler2
import OAI.Combinatorics.MatchingCount.Sampling.FiniteSampler3
import OAI.Combinatorics.MatchingCount.Sampling.FiniteSampler4
import OAI.Combinatorics.MatchingCount.Algorithm.GuardBudget
import OAI.Combinatorics.MatchingCount.Machines.ProgramComposition
import OAI.Combinatorics.MatchingCount.Graphs.Output
import OAI.Combinatorics.MatchingCount.Arithmetic.TreeDivision
import OAI.Combinatorics.MatchingCount.Machines.TreeLanguage
import OAI.Combinatorics.MatchingCount.Sampling.TreeUnitCorrect
import OAI.Combinatorics.MatchingCount.Tapes.RandomReservoir
import OAI.Combinatorics.MatchingCount.Complexity.PhysicalCost
import OAI.Combinatorics.MatchingCount.Probability.MainLaw
namespace OAI
namespace MatchingFPRAS
theorem thm_main : MainStatement := by
obtain ⟨C,d,hC,hbound⟩:=LiteralPhysical.mainTime_bound
refine ⟨LiteralPhysical.mainProgram.machine,C,d,hC,?_⟩
intro G ε δ he he1 hd _hd1
dsimp only
have hn:=hbound G ε δ he he1 hd.le
obtain ⟨hp,hz⟩:=LiteralPhysical.mainProgram_outputs G ε δ he he1 hd.le
(timeBound C d G ε δ) hn
exact ⟨hp,hz,LiteralPhysical.mainProgram_success G ε δ he he1 hd
(timeBound C d G ε δ) hn⟩
end MatchingFPRAS
end OAI
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