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ComplementedSubspace/ComplexCorollary.lean

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1import ComplementedSubspace.ComplexProjectionRealEquiv
2import ComplementedSubspace.ComplexCorollaryAssembly
3
4/-! The complex unconditional-basis theorem, using the actual finite complex
5projection and a whole-space real equivalence to the verified real frame sum.
6The continuous dual is handled by the real/complex dual isometry. -/
7
8noncomputable section
9set_option backward.isDefEq.respectTransparency false
10set_option backward.isDefEq.respectTransparency.types false
11set_option synthInstance.maxSize 256
12
13namespace ComplementedSubspace
14
15/-- For every positive tolerance there is a projection on a complex Banach
16space with an actual 1-unconditional basis, of norm below one plus that
17tolerance, whose range and continuous dual have no unconditional basis. -/
18theorem complexCorollary : ComplexCorollaryStatement := by
19 exact complexCorollary_of_recursive_range_equivalences
20 (fun s => ⟨s.predecessorComplexRangeRealEquiv⟩)
21
22end ComplementedSubspace