Proof of `Joint binary projections for commuting idempotents`
groundedproofs/Lax342547Proofs/JointProjectors.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
Work in the commutative algebra generated by the operators. Products of the selected operators and their complements give mutually annihilating idempotents whose sum is the identity. Their ranges give a linear decomposition, so their dimensions add and bound the number of nonzero labels.