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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 | import OAI.LinearAlgebra.MatrixMultiplication.FieldGroups.NativeLaws
namespace OAI
/-! Group assignments, orbit counts and extraction capacities. -/
noncomputable section
namespace MatrixMultiplication.AllFieldGroupBranchDesignation
open AllFieldHistory AllFieldHistoryChildLaws AllFieldGroupOrbitData
open AllFieldGroupNativeLaws
attribute [local instance] Classical.propDecidable Classical.decEq
def nativeBranchDesignated {K : ℕ} (w : Work K) (right : Bool)
(side : Fin 3) (b : w.Branch) : Prop :=
w.stage ≠ 2 ∧ AllFieldNativeCapacity.designated w.priority side
(halfShape w.parentShape (w.splitShape b) right)
theorem sharing_iff_stage_ne_two {K tick : ℕ} {sigma : Placement}
(h : ActiveOrder K tick sigma) :
sharing h = true ↔ h.val.val.1.stage ≠ 2 := by
rcases h with ⟨⟨⟨work, _⟩, _⟩, _⟩
cases work <;> simp [sharing, Work.stage]
theorem order_branch_childWeight {K tick : ℕ} {sigma : Placement}
(right : Bool) (h : ActiveOrder K tick sigma) (side : Fin 3)
(b : h.val.val.1.Branch) :
childWeight right h.val (branchShape h.val.val b) (sigma side) =
(halfShape h.val.val.1.parentShape (h.val.val.1.splitShape b) right)
(h.val.val.1.priority side) := by
rw [← halfShape_childWeight, canonicalChildShape_branchShape,
placement_symm_order_side]
theorem designated_branchShape {K tick : ℕ} {sigma : Placement}
(right : Bool) (side : Fin 3) (h : ActiveOrder K tick sigma)
(hside : side ≠ 0) (b : h.val.val.1.Branch) :
AllFieldGroupOrbitData.designated right side sigma h (branchShape h.val.val b) ↔
nativeBranchDesignated h.val.val.1 right side b := by
change (sharing h = true ∧
(if side = 1 then childWeight right h.val (branchShape h.val.val b) (sigma 2) = 0
else if side = 2 then
childWeight right h.val (branchShape h.val.val b) (sigma 0) *
childWeight right h.val (branchShape h.val.val b) (sigma 1) = 0
else False)) ↔ _
rw [sharing_iff_stage_ne_two]
simp only [order_branch_childWeight, nativeBranchDesignated,
AllFieldNativeCapacity.designated]
fin_cases side
· exact False.elim (hside rfl)
· simp
· simp
end MatrixMultiplication.AllFieldGroupBranchDesignation
end
end OAI
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