Proof of `Rank loss under restriction of a bilinear form` (2nd statement)
groundedproofs/Lax342547Proofs/RestrictionRank.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
Restricting the domain loses at most the subspace codimension. Restricting the output functional to that subspace loses at most the dimension of its annihilator, which is the same codimension. Rank-nullity combines the two losses.