Manuscript XVI-B@1 · XVI-B.tex · proposition · 6a0abffd

Proposition: Conditional transfer of the frozen obstruction

The correct XI-G transfer statement · lines 509–535 · proof included or linked

XVI-B@1#prop:transfer, XVI-B@1#eq:same-class

Suppose an actual prepared observable kernel $w_{D} \in K$ has been constructed. If

w_{D} - w_{0} \in I_{sol},

then

[w_{D}]_{sol} = [w_{0}]_{sol},

and (eq:old-obstruction) transfers to $w_{D}$ .

Proof. Linearity of the pairings makes $I_{sol}$ a vector subspace. Consequently

w_{D} + I_{sol} = w_{0} + (w_{D} - w_{0}) + I_{sol} = w_{0} + I_{sol} .

The asserted obstruction follows from (eq:old-obstruction).

Displayed formulas in this passage

XVI-B@1#eq:same-class · line 514
$w_{D} - w_{0} \in I_{sol},$
unlabeled · line 519
$[w_{D}]_{sol} = [w_{0}]_{sol},$
unlabeled · line 528
$w_{D} + I_{sol} = w_{0} + (w_{D} - w_{0}) + I_{sol} = w_{0} + I_{sol} .$