Proof of `Rank loss under restriction of a bilinear form` (1st 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
Factor the row map through its image. Pullback along the resulting surjection preserves rank, because its dual is injective. The only loss is restriction to the image, which costs at most twice its codimension.