Proof of `Exact image pins in nominal coefficient spaces` (5th 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
The third isomorphism theorem and rank-nullity identify the increase in each stored pin dimension with the tested span's dimension in the old nominal quotient. Summing gives the exact rank increment.