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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 | import Mathlib
import OAI.Combinatorics.MatchingCount.Algorithm.RationalEstimator
namespace OAI
namespace MatchingFPRAS.FiniteTrial
variable {G : GraphInput} [Nontrivial (Fin G.n)]
def sampleCount (p : Trial.Parameters G) : ℕ :=
⌈10*(Counting.sigma (sourceD (G:=G) p.K) p.K p.epsilon)⁻¹^2*((G.n:ℚ)+p.K+1)⌉₊
omit [Nontrivial (Fin G.n)] in
lemma sampleCount_eq (p : Trial.Parameters G) : sampleCount p=p.S := by
unfold sampleCount Trial.Parameters.S Enlargement.stageSampleCount
apply Nat.ceil_congr
intro s
unfold Trial.Parameters.D
rw [←sourceD_eq (G:=G)]
have hh:=Counting.sigma_cast (sourceD (G:=G) p.K) p.K p.epsilon
rw [←hh]
exact_mod_cast Iff.rfl
end MatchingFPRAS.FiniteTrial
end OAI
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