Proof of `Independent ordered mixer blocks at distinct labels` (3rd statement)
groundedproofs/Lax342547Proofs/OrderedMixerLaw.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
Select an index with a nonzero ordered coefficient. Its observation can realize any target while the other matrices are zero, so the full parity map is a surjective linear map on the independent matrix family.