Proof of `Random sharp-block forms and their alternating parity` (3rd statement)
groundedproofs/Lax342547Proofs/SharpMixerLaw.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
Push the uniform family of sharp mixers through its nonzero label-weighted sum. The forward and reverse ranks obey the square-matrix count; their alternating sum obeys the disjoint-block count proved above.