Integrated Route195 kernel+pushout lowering on the Route192 baseline #
This route keeps Route192's candidate actual split and target Route28 literal quotient/action route. It combines the two Route194 Section 7 lowerings:
- the five Route78 selected kernel/Frattini packets are replaced by the five
Route67 Lemma 7.2 packets from
Section7KernelRoute194Closers; minimalBlock_preheadCentralPushoutSquarePolarDatais replaced by the more concreteminimalBlock_preheadActualScalarCentralPushoutData.
theorem
Q2Presentation.Induction.centralCover_realization_proven_fine_from_selfGroupTowerCurrentIntegrated195KernelPushoutRoute192
{p : FramedPair}
{chief : NonScalarChiefFactor p}
(G : MinimalBlockGroupTowerData p chief)
(h : ¬ScalarTerminal p)
(Fdet : MinimalBlockPreheadExtraspecialEquivariantFamilyData G.preheadTowerData)
(A : MinimalBlockPreheadExtraspecialAnnihilationData Fdet)
(Rdet : MinimalBlockPreheadExtraspecialRadicalData Fdet)
:
Nonempty (CoverRealization (G.toMinimalBlock h Fdet A Rdet))
theorem
Q2Presentation.Induction.boundaryFramed_recursive_branch_from_fourier_currentIntegrated195KernelPushoutRoute192
(p : FramedPair)
(h : ¬ScalarTerminal p)
:
∃ (children : List FramedPair) (combine : List Cardinal.{0} → Cardinal.{0}),
(∀ c ∈ children, framedMeasure c < framedMeasure p) ∧ framedCountA p = combine (List.map framedCountA children) ∧ framedCountQ p = combine (List.map framedCountQ children)
theorem
Q2Presentation.Induction.boundaryFramed_recursion_step_currentIntegrated195KernelPushoutRoute192
(p : FramedPair)
:
framedCountA p = framedCountQ p ∨ ∃ (children : List FramedPair) (combine : List Cardinal.{0} → Cardinal.{0}),
(∀ c ∈ children, framedMeasure c < framedMeasure p) ∧ framedCountA p = combine (List.map framedCountA children) ∧ framedCountQ p = combine (List.map framedCountQ children)
theorem
Q2Presentation.Induction.finite_surjection_counts_equal_currentIntegrated195KernelPushoutRoute192
(G : Type)
[Group G]
[Finite G]
[Nonempty G]
: