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e3e0a0d | 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 | import OAI.SetTheory.PartitionPrinciple.Geometry.CompressionExternalTileOverlaps
import OAI.SetTheory.PartitionPrinciple.Geometry.RequestedOwnerSlotLaws
namespace OAI
section
namespace PartitionPilot.Forcing.GroundCompressionCompletion
open SetRealization Compression.RecursiveMaps.TileRequests
universe u
variable {M : TransitiveGround.{u}} {initial : RecursiveStateData.{u}}
variable {I Sources Reps G m inv one T τ P0 r0 μ0 A0 : ZFSet.{u}}
variable (completion : GroundCompressionCompletion M initial I Sources Reps G m one T τ)
variable (group : GroupCode G m inv one) (oldAction : PosetActionCode G P0 m one r0 A0)
variable (compression : CompressionOriginalData P0 r0 μ0 A0 G
(completion.algebra.union.fields 0) (completion.algebra.union.fields 1)
(completion.algebra.union.fields 2) (completion.algebra.union.fields 12))
theorem externalFamilyVertexCode_eq_slot
(r : ExternalRequestIndex I P0 (externalRectangles P0 G r0 μ0 A0))
(i : Option ((completion.externalFamily group oldAction compression).Child r)) :
completion.externalFamilyVertexCode group oldAction compression r i =
natSetCode (((completion.externalFamily group oldAction compression).request r).vertexSlot i) := by
cases r with
| inl r => cases i <;> rfl
| inr r =>
cases r with
| inl r => cases i <;> rfl
| inr r =>
cases i with
| none => rfl
| some b => cases b with | up b => cases b <;> rfl
end PartitionPilot.Forcing.GroundCompressionCompletion
end
end OAI
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