{"traversal_complete": true,
 "target_type_whnf":
 "∀ (ρ : ℝ),\n  0 < ρ →\n    ∃ a,\n      TopologicalSpace.SeparableSpace ↥(ComplementedSubspace.Ambient a) ∧\n        UniformConvexSpace ↥(ComplementedSubspace.Ambient a) ∧\n          ComplementedSubspace.HasRealBanachLatticeOrder ↥(ComplementedSubspace.Ambient a) ∧\n            ∃ P,\n              P ∘SL P = P ∧\n                ‖P‖ < 1 + ρ ∧\n                  ‖ContinuousLinearMap.id ℝ ↥(ComplementedSubspace.Ambient a) - P‖ < 1 + ρ ∧\n                    ComplementedSubspace.HasSeparatedRange P ∧\n                      ComplementedSubspace.HasSeparatedRange\n                        (ContinuousLinearMap.id ℝ ↥(ComplementedSubspace.Ambient a) - P)",
 "target_type": "ComplementedSubspace.RealMainTheoremStatement",
 "target_level_parameters": [],
 "target_kind": "theorem",
 "target": "ComplementedSubspace.realMainTheorem",
 "reachable_project_axiom_opaque_unsafe_partial": [],
 "reachable_axioms_stock_collectAxioms":
 ["propext", "Classical.choice", "Quot.sound"],
 "reachable_axioms_direct_traversal":
 ["propext", "Classical.choice", "Quot.sound"],
 "queued_nodes": 40291,
 "project_origin_modules":
 ["BanLat.Basic",
  "BanLat.Disjoint",
  "BanLat.Dual",
  "BanLat.Normed",
  "BanLat.OrderComplete",
  "BanLat.RieszDec",
  "ComplementedSubspace.ActualProjectionDPR",
  "ComplementedSubspace.ActualProjectionDualDPR",
  "ComplementedSubspace.Ambient",
  "ComplementedSubspace.AmbientBasis",
  "ComplementedSubspace.AmbientFiniteApproximation",
  "ComplementedSubspace.AmbientLattice",
  "ComplementedSubspace.AmbientProjection",
  "ComplementedSubspace.AmbientSeparable",
  "ComplementedSubspace.AmbientUniformConvex",
  "ComplementedSubspace.BasisRestriction",
  "ComplementedSubspace.BasisTransport",
  "ComplementedSubspace.DPRObstruction",
  "ComplementedSubspace.DPRtoGL",
  "ComplementedSubspace.DiagonalFrameProduct",
  "ComplementedSubspace.DiagonalFrameSummand",
  "ComplementedSubspace.FiniteApproximation",
  "ComplementedSubspace.FiniteBasisTraceBound",
  "ComplementedSubspace.FiniteBidual",
  "ComplementedSubspace.FiniteBlockDPRLower",
  "ComplementedSubspace.FiniteBlockObstruction",
  "ComplementedSubspace.FiniteCoordinateSelection",
  "ComplementedSubspace.FiniteCorrection",
  "ComplementedSubspace.FiniteDualBasis",
  "ComplementedSubspace.FiniteDualDPRLower",
  "ComplementedSubspace.FiniteDualSuperspace",
  "ComplementedSubspace.FiniteFrame",
  "ComplementedSubspace.FiniteHeadHilbert",
  "ComplementedSubspace.FiniteHilbertAverage",
  "ComplementedSubspace.FiniteLpGeometry",
  "ComplementedSubspace.FiniteOverlapBasisColumns",
  "ComplementedSubspace.FiniteOverlapBound",
  "ComplementedSubspace.FiniteOverlapConclusion",
  "ComplementedSubspace.FiniteOverlapDualScale",
  "ComplementedSubspace.FiniteOverlapGoodSecond",
  "ComplementedSubspace.FiniteOverlapLp",
  "ComplementedSubspace.FiniteOverlapMatrixNorms",
  "ComplementedSubspace.FiniteOverlapMoments",
  "ComplementedSubspace.FiniteOverlapObstruction",
  "ComplementedSubspace.FiniteOverlapRandomization",
  "ComplementedSubspace.FiniteOverlapScale",
  "ComplementedSubspace.FiniteOverlapUpper",
  "ComplementedSubspace.FiniteParameterBounds",
  "ComplementedSubspace.FiniteParameterGap",
  "ComplementedSubspace.FiniteProductObstruction",
  "ComplementedSubspace.FiniteProjectionTrace",
  "ComplementedSubspace.FiniteSelectedHilbertModel",
  "ComplementedSubspace.FiniteSelectionCoordinates",
  "ComplementedSubspace.FiniteSigns",
  "ComplementedSubspace.FiniteSignsInterpolation",
  "ComplementedSubspace.FiniteSuperspaceSplitting",
  "ComplementedSubspace.FiniteTraceOverlap",
  "ComplementedSubspace.FiniteTraceSelection",
  "ComplementedSubspace.FrameCoefficient",
  "ComplementedSubspace.FrameCoefficientHilbert",
  "ComplementedSubspace.FrameCoefficientNorm",
  "ComplementedSubspace.FrameCoefficientRange",
  "ComplementedSubspace.FrameCoefficientReindexedRange",
  "ComplementedSubspace.FrameProjectionNorm",
  "ComplementedSubspace.FrameProjectionRange",
  "ComplementedSubspace.GLDualRetraction",
  "ComplementedSubspace.GLRetraction",
  "ComplementedSubspace.HilbertComplement",
  "ComplementedSubspace.HilbertOverlap",
  "ComplementedSubspace.HilbertTraceTransfer",
  "ComplementedSubspace.IsometricProductSplitting",
  "ComplementedSubspace.LatticeApproximation",
  "ComplementedSubspace.LatticeBasis",
  "ComplementedSubspace.LatticeSpectral",
  "ComplementedSubspace.LocalHilbert",
  "ComplementedSubspace.LocalHilbertCompactness",
  "ComplementedSubspace.LocalHilbertCoordinates",
  "ComplementedSubspace.LocalHilbertDual",
  "ComplementedSubspace.LocalHilbertEmbeddedRenorm",
  "ComplementedSubspace.LocalHilbertFactorization",
  "ComplementedSubspace.LocalHilbertHeadRenorm",
  "ComplementedSubspace.LocalHilbertProjection",
  "ComplementedSubspace.LocalHilbertProperty",
  "ComplementedSubspace.LocalHilbertQuotient",
  "ComplementedSubspace.LocalHilbertRecursiveKernelDual",
  "ComplementedSubspace.LocalHilbertSum",
  "ComplementedSubspace.LocalHilbertSumDual",
  "ComplementedSubspace.LocalHilbertTransport",
  "ComplementedSubspace.LocalUnconditional",
  "ComplementedSubspace.LpHeadTail",
  "ComplementedSubspace.LpSubmodule",
  "ComplementedSubspace.LpTwoParallelogram",
  "ComplementedSubspace.LpTwoUniformConvex",
  "ComplementedSubspace.NormSqSplitting",
  "ComplementedSubspace.NormalizedHilbertSynthesis",
  "ComplementedSubspace.ProductFrame",
  "ComplementedSubspace.ProductFrameIndex",
  "ComplementedSubspace.ProductFrameLp",
  "ComplementedSubspace.ProductFrameMoments",
  "ComplementedSubspace.ProductFrameRowWitness",
  "ComplementedSubspace.ProductFrameSignContraction",
  "ComplementedSubspace.ProductFrameSignSample",
  "ComplementedSubspace.ProductFrameSymmetry",
  "ComplementedSubspace.ProductFrameTrace",
  "ComplementedSubspace.ProductFrameTraceBound",
  "ComplementedSubspace.ProductFrameWitness",
  "ComplementedSubspace.ProjectionCorollaries",
  "ComplementedSubspace.ProjectionOverlapLower",
  "ComplementedSubspace.ProjectionPerturbation",
  "ComplementedSubspace.RealMainTheorem",
  "ComplementedSubspace.RecursiveDiagonalDPR",
  "ComplementedSubspace.RecursiveDiagonalDualDPR",
  "ComplementedSubspace.RecursiveHeadHilbert",
  "ComplementedSubspace.RecursiveKernelHilbert",
  "ComplementedSubspace.RecursiveParameters",
  "ComplementedSubspace.RecursiveProjection",
  "ComplementedSubspace.RecursiveTailHilbert",
  "ComplementedSubspace.ReindexedFrameProjection",
  "ComplementedSubspace.SelectedCoefficientHilbert",
  "ComplementedSubspace.SelectedHilbertReplacement",
  "ComplementedSubspace.SelectedProjectionSetup",
  "ComplementedSubspace.TensorMoment",
  "ComplementedSubspace.TensorProjection",
  "ComplementedSubspace.TheoremStatement",
  "ComplementedSubspace.UnconditionalHilbertSynthesis",
  "BanLat.Operators.OrderBounded",
  "BanLat.Operators.Positive",
  "BanLat.Operators.RieszKantorovich",
  "BanLat.Substructures.Ideal",
  "BanLat.Substructures.Sublattice",
  "BanLat.Substructures.Band.Basic",
  "BanLat.Substructures.Band.DisjointComplement",
  "BanLat.Substructures.Band.Generated",
  "BanLat.Substructures.Band.Lattice",
  "BanLat.Substructures.Band.PPP",
  "BanLat.Substructures.Band.Projection"],
 "project_constants": 1946,
 "processed_nodes": 40291,
 "ownership_classification_complete": true,
 "node_budget": 300000,
 "missing_expected_bodies": [],
 "missing_checked_constants": [],
 "edges": 1332580,
 "edge_semantics":
 "Types and values for definitions/theorems/opaque declarations; types for axioms/constructors/recursors; types and constructor edges for inductives; quotient primitives are leaves. Values requested with allowOpaque=true. No imported axiom cache is used by this traversal.",
 "edge_budget": 4000000,
 "constants_without_import_origin": [],
 "checked_constants": 40291,
 "axiom_cross_check_agrees": true}