File size: 1,916 Bytes
92416a2 | 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 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 | import OAI.Dynamics.ConditionalShuffle.SelectedSchedule
namespace OAI
noncomputable section
open scoped Classical
namespace Revealed.Instrument
open Thorp Thorp.Conditional
lemma Data.ext {E S G Ω : Type} {I J : Data E S G Ω}
(ho : I.obs = J.obs) (hi : I.inc = J.inc) (hn : I.next = J.next) : I = J := by
cases I
cases J
cases ho
cases hi
cases hn
rfl
variable {E E' S G Ω : Type} [fintype_S : Fintype S] [fintype_G : Fintype G] [group_G : Group G] [fintype_Ω : Fintype Ω] [nonempty_Ω : Nonempty Ω]
variable (I : Data E S G Ω) (J : Data E' S G Ω) (f : E → E')
(ho : ∀ e c, J.obs (f e) c = I.obs e c)
(hi : ∀ e c, J.inc (f e) c = I.inc e c)
(hn : ∀ e s, J.next (f e) s = f (I.next e s))
include hn
lemma map_base (e : E) (n : ℕ) (p : Fin n → S) :
base J (f e) n p = f (base I e n p) := by
let retained_fintype_S := fintype_S
let retained_fintype_G := fintype_G
let retained_group_G := group_G
let retained_fintype_Ω := fintype_Ω
let retained_nonempty_Ω := nonempty_Ω
induction n with
| zero => rfl
| succ n ih => rw [base, ih, hn]; rfl
include ho
lemma map_observed (e : E) (n : ℕ) (c : Fin n → Ω) :
observed J (f e) n c = observed I e n c := by
induction n with
| zero => rfl
| succ n ih =>
simp only [observed, ih, map_base I J f hn, ho]
include hi
lemma map_groupRun (e : E) (n : ℕ) (c : Fin n → Ω) :
groupRun J (f e) n c = groupRun I e n c := by
induction n with
| zero => rfl
| succ n ih =>
simp only [groupRun, map_observed I J f ho hn, map_base I J f hn, hi, ih]
lemma map_distance (e : E) (n : ℕ) : distance J (f e) n = distance I e n := by
rw [distance_disintegration, distance_disintegration]
have hh : pathJoint J (f e) n = pathJoint I e n := by
unfold pathJoint
simp_rw [map_observed I J f ho hn, map_groupRun I J f ho hi hn]
rw [hh]
end Revealed.Instrument
end
end OAI
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