Manuscript En05-A@1 · En05-A.tex · proposition · f076e703
Proposition: Fixed-channel ordering invariance
Two retiming statements and a boost-closure limitation › Legal reorderings of fixed channels · lines 1474–1487 · proof included or linked
En05-A@1#prop:gateorder
Let a finite collection of fixed labelled channels have declared complete supports. Suppose a strict partial order makes all channels with intersecting supports comparable. Every legal linear extension has the same total channel.
Proof. Incomparable channels have disjoint supports and commute after extension by identities. Any two linear extensions of a finite partial order are connected by adjacent swaps of incomparable elements. Every swap preserves the channel composition.