Candidate Route147 pointwise closers #
Route147's integrated candidate side currently consumes
CandidateRoute146Closers, whose remaining Section 8 assumptions are seven
pointwise scalar/Frattini atoms. This sidecar does not edit that integrated
route. It exposes a same-call-shape replacement provider whose proof bypasses those
seven pointwise atoms:
- scalar values and selected additivity are induced by the lower
R-valued obstruction map on the middle exact-image source; - base/fibre coordinates, curried realization, and inverse laws are induced by the lower Frattini affine-fibre exact-image partition.
The resulting closure is strictly lower than the Route147 pointwise frontier:
the final provider depends only on the two semantic Section 8 leaves
centralCover_candidateObstructionMapData and
centralCover_candidateFrattiniExactImageCardinalityData, plus Lean standard
axioms.
Scalar pointwise values from the middle R-obstruction #
Route147 scalar value at one point, obtained by evaluating the selected
R-obstruction against lambda : B.XR.
Equations
- D.route147ScalarPushoutValueAtPointData lam x = { value := (D.obstruction x) lam }
Instances For
Route147 scalar value packet for one scalar, induced by the selected
middle R-obstruction.
Equations
- D.route147NonzeroScalarPushoutValueAtData lam = { valueAt := fun (x : Q2Presentation.Induction.centralCoverCandidateMiddleSource T) => (D.obstruction x) lam }
Instances For
The selected Route147 scalar-pushout family induced by the lower
R-obstruction map.
Equations
- D.route147ScalarPushoutFamilyData = { valueAt := fun (lam : ↥B.XR) => (D.route147NonzeroScalarPushoutValueAtData lam).valueData }
Instances For
Pointwise additivity for the selected Route147 scalar family. This closes the pointwise additivity shape after replacing the arbitrary family by the family induced by the semantic obstruction map.
Equations
- D.route147NonzeroDistinctAdditivityAtData x lam mu hlam hmu hdiff = { map_add_at := ⋯ }
Instances For
Nonzero-distinct additivity for the selected Route147 scalar family.
Equations
- D.route147NonzeroDistinctAdditivityData = { map_add_nonzero_distinct := ⋯ }
Instances For
Route106-shaped scalar packet induced by the lower middle obstruction.
Equations
- D.route147ScalarPushoutData = { scalarFamily := D.route147ScalarPushoutFamilyData, zero_value := ⋯, additivityNonzeroDistinct := D.route147NonzeroDistinctAdditivityData }
Instances For
The Route147 pointwise scalar-value atom is closed from the lower semantic
middle R-obstruction map.
The nonzero scalar value packet assembled from theorem-level pointwise values induced by the same lower obstruction map.
Selected pointwise additivity: the arbitrary-family Route147 additivity atom is strictly lowered to the family induced by the semantic obstruction map.
Selected scalar family with nonzero-distinct additivity, strictly below the arbitrary-family Route147 pointwise additivity atom.
Route147 scalar packet from the lower middle obstruction.
Frattini pointwise data from the affine-fibre partition #
Pointwise base coordinate induced by the selected Frattini partition.
Instances For
Base coordinate map induced by the selected Frattini partition.
Equations
- P.route147BaseCoordinateData = { baseCoordinate := fun (f : Q2Presentation.Induction.centralCoverCandidateSource) => (P.route147BaseCoordinateAtData f).baseCoordinateAt }
Instances For
Pointwise fibre coordinate over the selected Route147 base coordinate.
Instances For
Fibre coordinate map over the selected Route147 base coordinate.
Equations
- P.route147FiberCoordinateData = { fiberCoordinate := fun (f : Q2Presentation.Induction.centralCoverCandidateSource) => (P.route147FiberCoordinateAtData f).fiberCoordinateAt }
Instances For
Pointwise realization induced by the inverse of the selected Frattini partition.
Instances For
Curried realization induced by the inverse of the selected Frattini partition.
Equations
- One or more equations did not get rendered due to their size.
Instances For
Pointwise realization-after-coordinate law for the selected Route147 coordinates.
Equations
- P.route147RealizeLiftCoordinateAtData f = { realize_liftCoordinate_at := ⋯ }
Instances For
Realization-after-coordinate law for the selected Route147 coordinates.
Equations
- P.route147RealizeLiftCoordinateData = { realize_liftCoordinate := ⋯ }
Instances For
Pointwise coordinate-after-realization law for the selected Route147 coordinates.
Equations
- P.route147LiftCoordinateRealizeAtData y = { liftCoordinate_realize_at := ⋯ }
Instances For
Coordinate-after-realization law for the selected Route147 coordinates.
Equations
- P.route147LiftCoordinateRealizeData = { liftCoordinate_realize := ⋯ }
Instances For
Route85-shaped Frattini coordinate system induced by the selected Route147 affine-fibre partition.
Equations
- One or more equations did not get rendered due to their size.
Instances For
The Route147 pointwise Frattini base-coordinate atom is closed from the lower affine-fibre exact-image partition.
Selected pointwise Frattini fibre-coordinate data. The original Route147 atom is over an arbitrary base-coordinate map; here it is lowered to the base coordinate induced by the semantic Frattini partition.
The Route147 pointwise Frattini realization atom is closed from the inverse of the lower affine-fibre exact-image partition.
Selected pointwise realization-after-coordinate law.
Selected pointwise coordinate-after-realization law.
Route147 Frattini coordinate system for a supplied middle obstruction, assembled from the lower affine-fibre exact-image partition.
Route147 pointwise reassembly #
Coherent Route147 packet: selected scalar data and selected Frattini coordinate data attached to the same lower middle obstruction map.
- middleObstruction : CentralCoverCandidateMiddleRLiftObstructionMapData B T
- scalar : CentralCoverCandidateRoute106ScalarPushoutData B T
- frattini : CentralCoverCandidateRoute85FrattiniCoordinateSystemData B T self.middleObstruction
Instances For
Reassemble direct exact-image residual data from Route147 pointwise lowerings.
Equations
- S.directExactImageResidualData = { middleObstruction := S.middleObstruction, frattiniPartition := S.frattini.frattiniExactImage }
Instances For
Reassemble the candidate lift partition from Route147 pointwise lowerings and the route-supplied quotient-frame map.
Equations
Instances For
Coherent Route147 pointwise-lowered data.
Direct exact-image residual data with the Route147 pointwise atoms lowered through semantic obstruction and Frattini partition packets.
Drop-in Route147 candidate lift-partition provider.
This has the same B T Q call shape as
centralCover_candidateLiftPartitionData_from_candidateRoute146Closers.
Canonical-tower spelling matching integrated routes that keep the canonical quotient tower in scope.
Audit surface exposing the selected Route147 packet together with the route-ready lift partition it determines.