Proof of `Actual paired-witness key spaces satisfy the baseline hypotheses` (1st statement)
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
Indexed sparse exclusion shows that even the span of all selected rays is disjoint from the table. The component's incident key span is a subspace of that span. Apply the same argument after reversing the units.