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d5b7741 | 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 | import OAI.Combinatorics.ContingencyTables.Sampling.ProfileTransitionCount
namespace OAI
/-! # A completion-coordinate change in the finite transition count -/
namespace ContingencyTables.IntegerLaw
open scoped BigOperators Classical
noncomputable section
lemma booleanFinish_equiv_count {A B C : Type*} [Fintype A] [Fintype B] [Fintype C]
[DecidableEq C] {s f Q : ℕ} (p : IntegerLaw A (2^f)) (q : IntegerLaw B Q)
(e : A ≃ B) (M : ℕ) (finish : (Fin s → Bool) → B → C)
(h : ∀ a,p.count a=q.count (e a)*M) (c : C) :
(booleanFinish p (fun bits a => finish bits (e a))).count c=
∑ bits : Fin s → Bool,∑ b,if finish bits b=c then q.count b*M else 0 := by
rw [booleanFinish_count]
simp_rw [h]
apply Finset.sum_congr rfl
intro bits _
exact e.sum_comp (fun b : B => if finish bits b=c then q.count b*M else 0)
end
end ContingencyTables.IntegerLaw
end OAI
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