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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 | import Mathlib
import OAI.Combinatorics.MatchingCount.Machines.OnlineUniform
namespace OAI
namespace MatchingFPRAS.PhysicalStream
open Finset Variation
variable {A B C : Type} [Fintype A] [Fintype B] [Fintype C]
lemma qaverage_imageLaw (f : A→B) (h : B→ℚ) :
((qaverage (fun a=>h (f a)) : ℚ):ℝ)=∑ b,imageLaw f b*(h b:ℝ) := by
classical
unfold imageLaw push uniform
simp only [sum_mul,ite_mul,zero_mul]
rw [sum_comm]
simp only [sum_ite_eq,mem_univ,ite_true,one_div,inv_mul_eq_div]
unfold qaverage
push_cast
rw [sum_div]
lemma qaverage_eq_of_imageLaw_eq (f : A→C) (g : B→C)
(he : imageLaw f=imageLaw g) (h : C→ℚ) :
qaverage (fun a=>h (f a))=qaverage (fun b=>h (g b)) := by
apply Rat.cast_injective (α:=ℝ)
rw [qaverage_imageLaw,qaverage_imageLaw,he]
end MatchingFPRAS.PhysicalStream
end OAI
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