Lax Lean Archive

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Proof of `Measurable bases and measurable splittings of subspaces` (3rd statement)

groundedproofs/Lax606786Proofs/GrassmannianContraction.lean · lax-606786

What this proof establishes

thm✓Lax606786.MeasurableBases (3rd statement)

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitLab

Description

The construction of existsmeasurableretractexists_measurable_retract produces both at once: the selected unit vector of each subspace is the one the chosen functional does not kill, so it spans a complement of the retracted subspace.