openAI-math-dataset / lean /OAI /SetTheory /PartitionPrinciple /Definability /ExternalFamilySlotCodes.lean
| 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 | |