Proof of `Independent free-direction spaces at distinct selector labels` (2nd statement)
groundedproofs/Lax342547Proofs/AtomDirections.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 a bit on which the labels differ. The empty-selector equation gives u+v, and the singleton-selector equation gives s_a u+t_a v. Their nonzero determinant recovers u and v coordinate by coordinate.