OAI/Analysis/Nonexpansive/NormalizedContradiction.lean
2 declarations, 0 contain sorry, 0 declared as axioms
The actual tree and switching contradiction for normalized minimal data
The adaptive producer constructs the tree without an added geometric premise. Its actual finite switching witnesses lie in the whole difference ball, and the branch argument contradicts the produced dense-point detectors there.
- theorem
OAI.ReflexiveFixedPoints.SwitchingTreeData.contradictionline 24Source documentation
The concrete constructed tree cannot coexist with normalized minimal data.
theorem contradiction {D : NormalizedMinimalData (X := X)} (A : SwitchingTreeData D) : …Mentions: OAI.ReflexiveFixedPoints.NormalizedMinimalData, OAI.ReflexiveFixedPoints.SwitchingTreeData
- theorem
OAI.ReflexiveFixedPoints.normalizedMinimalData_falseline 41Source documentation
No normalized minimal invariant counterexample exists. This calls the actual adaptive-tree producer and the fully discharged finite switching proof.
theorem normalizedMinimalData_false (D : NormalizedMinimalData (X := X)) : False := by …