. Therefore, the dynamic meaning of D is unchanged in Λ/' i.e. M
d
(D) =
M'
d
(D).
Then clearly M'
d
(p
d
)(c) CM
d
(p
d
)(c) for all c ΕH
c
n
.
Now we show that Λ/' is a model of Δ. Since Λ/' is identical to Ν except on the
dynamic meaning of p
d
, we only have to show that Λ/' satisfies every update
rule in Δ. Consider any update rule τ in Δ. Three cases arise.
Case (a): τ is the given update rule (pß)) D. Then clearly, τ is true in Λ/'.
If τ is not the given update rule, then it is some other update rule (q
d
(t))
Case (b): Β contains a dynamic predicate that depends on p
d
. Since τ is true in
N, we have M
d
(B[s]) C M
d
(q
d
(t)[s]). ...
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