openAI-math-dataset / lean /OAI /SetTheory /PartitionPrinciple /Geometry /FixedCompressionSeeds.lean
| import OAI.SetTheory.PartitionPrinciple.Forcing.InitialRecursiveActionAgreement | |
| import OAI.SetTheory.PartitionPrinciple.Forcing.RecursiveNextTaskActions | |
| namespace OAI | |
| section | |
| namespace PartitionPilot.Forcing | |
| universe u | |
| structure FixedCompressionSeed | |
| (P r μ A τ I Sources Reps G m inv one T Filters : ZFSet.{u}) : Prop where | |
| originalOrder : MeetOrderCode P r μ | |
| originalAction : PosetActionCode G P m one r A | |
| top_mem : τ ∈ P | |
| sources : ZFSet.IsFunc I P Sources | |
| filters : FunctionGraphOn I Filters | |
| productAgreement : ∀ δ i j g h k a, | |
| ZFSet.pair (ZFSet.pair δ i) j ∈ T → ZFSet.pair i a ∈ Sources → | |
| ZFSet.pair i g ∈ Reps → ZFSet.pair j h ∈ Reps → | |
| ZFSet.pair (ZFSet.pair δ g) k ∈ m → ActionAgreementBelow P r A k h a | |
| positiveAgreement : ∀ g h v i j k F, | |
| ActionAgreementBelow P r A g h v → ZFSet.pair i F ∈ Filters → v ∈ F → | |
| ZFSet.pair (ZFSet.pair g i) j ∈ T → | |
| ZFSet.pair (ZFSet.pair h i) k ∈ T → j = k | |
| end PartitionPilot.Forcing | |
| end | |
| end OAI | |