Proof of `Removing selected atoms leaves only unselected component labels` (2nd statement)
groundedproofs/Lax342547Proofs/ResidualLabels.lean · lax-342547
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
Choose the scalar decompositions at both endpoints and subtract their actual selected atoms. Pure annihilation is preserved, and deleting the selected labels preserves the label and sum-of-ranks budgets and all Boolean moment identities of the surviving base blocks.