Proof of `Baseline bilinear extensions retaining all frozen rows and columns` (2nd statement)
groundedproofs/Lax342547Proofs/FrozenBaselines.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
The sum map from the table space and key space is injective, so choose a linear left inverse. Within the table choose a retraction to the stored pins. Their composite supplies the frozen part; subtracting it from the table retraction supplies the complementary part.