File size: 3,114 Bytes
cdec422 | 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 65 66 67 68 69 70 71 72 73 74 75 76 77 | import OAI.LinearAlgebra.MatrixMultiplication.FieldGroups.NativeLaws
namespace OAI
/-! Group assignments, orbit counts and extraction capacities. -/
noncomputable section
namespace MatrixMultiplication.AllFieldGroupCompatibility
open AllFieldHistory AllFieldHistoryChildLaws AllFieldHistoryGroupMasks
open AllFieldHistoryGroupedRecovery AllFieldGroupOrbitData
open JointPopulation JointCanonicalization
attribute [local instance] Classical.propDecidable
variable {K tick : ℕ}
theorem groupIdealSide_ownWord (allocation : Allocation) (m : ℕ) (ε : ℝ)
(sigma : Placement) (side : Fin 3)
(e : Targets (K := K) (tick := tick) allocation m sigma)
(w : Raw (K := K) (tick := tick) allocation m sigma)
(hw : groupIdealSide allocation m ε (sigma side) sigma e w) :
tripleSide side (AllFieldGroupOrbitData.coarse allocation m sigma e) =
ownWord allocation m sigma w := by
change tripleSide side
(reorder sigma (triple (Counts (K := K) (tick := tick) allocation m sigma) e)) = _
rw [tripleSide_reorder]
funext p
have hs : tripleSide (sigma side)
(triple (Counts (K := K) (tick := tick) allocation m sigma) e) p =
shapeSide (sigma side) ((e p.1).val p.2) := by
generalize sigma side = s
fin_cases s <;> rfl
rw [hs]
exact (hw.1 p.1 p.2).symm
theorem groupIdealSide_fineCompatible (allocation : Allocation) (m : ℕ) (ε : ℝ)
(sigma : Placement) (side : Fin 3)
(e : Targets (K := K) (tick := tick) allocation m sigma)
(w : Raw (K := K) (tick := tick) allocation m sigma)
(hw : groupIdealSide allocation m ε (sigma side) sigma e w) :
fineCompatible allocation m ε sigma side e w := by
intro right h u hd
apply JointPopulationCompatibility.shape_count_window_of_typeWindow
(Counts (K := K) (tick := tick) allocation m sigma) e h u
(fun i => statistic h.val (if right then (w h i).2 else (w h i).1))
(compatibilityLaw right side sigma h u) (AllFieldHistoryMasks.childWidth ε h.val)
intro hu
rw [AllFieldGroupNativeLaws.compatibilityLaw_eq allocation m sigma right side h u hu hd]
cases right
· exact (hw.2 h u hu).1
· exact (hw.2 h u hu).2
theorem groupIdealSide_compatible (allocation : Allocation) (m : ℕ) (ε : ℝ)
(sigma : Placement) (side : Fin 3)
(e : Targets (K := K) (tick := tick) allocation m sigma)
(w : Raw (K := K) (tick := tick) allocation m sigma)
(hw : groupIdealSide allocation m ε (sigma side) sigma e w) :
Compatible allocation m ε sigma side e w :=
⟨groupIdealSide_ownWord allocation m ε sigma side e w hw,
groupIdealSide_fineCompatible allocation m ε sigma side e w hw⟩
theorem admissible_compatible (allocation : Allocation) (m : ℕ) (ε : ℝ)
(sigma : Placement) (side : Fin 3)
(e : Targets (K := K) (tick := tick) allocation m sigma)
(w : Raw (K := K) (tick := tick) allocation m sigma)
(hw : Admissible allocation m ε sigma side e w) :
Compatible allocation m ε sigma side e w :=
groupIdealSide_compatible allocation m ε sigma side e w hw.1
end MatrixMultiplication.AllFieldGroupCompatibility
end
end OAI
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