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Commits
206b1ee2
Commit
206b1ee2
authored
Dec 22, 2017
by
Florian Perlié-Long
Committed by
Alexandre Duret-Lutz
Jan 19, 2018
Browse files
* doc/tl/tl.tex: Typos
parent
0d26b5d2
Changes
1
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doc/tl/tl.tex
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206b1ee2
...
...
@@ -1481,8 +1481,8 @@ operator's arguments. For instance $\F\G(a)\AND \G(b) \AND \F\G(c) \AND
The following more complicated rules are generalizations of
$
f
\AND
\X\G
f
\equiv
\G
f
$
and
$
f
\OR
\X\F
f
\equiv
\F
f
$
:
\begin{align*}
f
\AND
\X
(
\G
(f
\AND
g
\ldots
)
\AND
h
\ldots
)
&
\equiv
\G
(f)
\AND
\X
(
\G
(g
\ldots
)
\AND
h
\ldots
)
\\
f
\OR
\X
(
\F
(f)
\OR
h
\ldots
)
&
\equiv
\F
(f)
\OR
\X
(h
\ldots
)
f
\AND
\X
(
\G
(f
\AND
g
\AND
\ldots
)
\AND
h
\AND
\ldots
)
&
\equiv
\G
(f)
\AND
\X
(
\G
(g
\AND
\ldots
)
\AND
h
\AND
\ldots
)
\\
f
\OR
\X
(
\F
(f)
\OR
h
\OR
\ldots
)
&
\equiv
\F
(f)
\OR
\X
(h
\OR
\ldots
)
\end{align*}
The latter rule for
$
f
\OR
\X
(
\F
(
f
)
\OR
h
\ldots
)
$
is only applied if all
$
\F
$
-formulas can be removed from the argument of
$
\X
$
with the
...
...
@@ -1685,9 +1685,9 @@ $q,\,q_i$ & a pure eventuality that is also purely universal \\
\begin{align*}
\G
(f
_
1
\AND\ldots\AND
f
_
n
\AND
\X
e
_
1
\AND
\ldots
\AND
\X
e
_
p)
&
\equiv
\G
(f
_
1
\AND\ldots\AND
f
_
n
\AND
e
_
1
\AND
\ldots
\AND
e
_
p)
\\
\G
(f
_
1
\AND\ldots\AND
f
_
n
\AND
\F
(g
_
1
\AND
\ldots
\AND
g
_
p
\AND
\X
e
_
1
\AND
\X
e
_
m))
&
\equiv
\G
(f
_
1
\AND\ldots\AND
f
_
n
\AND
\F
(g
_
1
\AND
\ldots
\AND
g
_
p)
\AND
e
_
1
\AND
\ldots
\AND
e
_
m)
\\
\F
(f
_
1
\OR\ldots\OR
f
_
n
\OR
\X
u
_
1
\OR
\ldots
\OR
\X
u
_
p)
&
\equiv
\F
(f
_
1
\OR\ldots\OR
f
_
n
\OR
u
_
1
\OR
\ldots
\
AND
u
_
p)
\\
\F
(f
_
1
\OR\ldots\OR
f
_
n
\OR
\G
(g
_
1
\OR
\ldots
\OR
g
_
p
\OR
\X
u
_
1
\OR
\X
u
_
m))
&
\equiv
\F
(f
_
1
\OR\ldots\AND
f
_
n
\OR
\G
(g
_
1
\OR
\ldots
\OR
g
_
p)
\OR
u
_
1
\OR
\ldots
\OR
u
_
m)
\\
\G
(f
_
1
\AND\ldots\AND
f
_
n
\AND
\F
(g
_
1
\AND
\ldots
\AND
g
_
p
\AND
\X
e
_
1
\AND
\ldots
\AND
\X
e
_
m))
&
\equiv
\G
(f
_
1
\AND\ldots\AND
f
_
n
\AND
\F
(g
_
1
\AND
\ldots
\AND
g
_
p)
\AND
e
_
1
\AND
\ldots
\AND
e
_
m)
\\
\F
(f
_
1
\OR\ldots\OR
f
_
n
\OR
\X
u
_
1
\OR
\ldots
\OR
\X
u
_
p)
&
\equiv
\F
(f
_
1
\OR\ldots\OR
f
_
n
\OR
u
_
1
\OR
\ldots
\
OR
u
_
p)
\\
\F
(f
_
1
\OR\ldots\OR
f
_
n
\OR
\G
(g
_
1
\OR
\ldots
\OR
g
_
p
\OR
\X
u
_
1
\OR
\ldots
\OR
\X
u
_
m))
&
\equiv
\F
(f
_
1
\OR\ldots\AND
f
_
n
\OR
\G
(g
_
1
\OR
\ldots
\OR
g
_
p)
\OR
u
_
1
\OR
\ldots
\OR
u
_
m)
\\
\G
(f
_
1
\OR\ldots\OR
f
_
n
\OR
q
_
1
\OR
\ldots
\OR
q
_
p)
&
\equiv
\G
(f
_
1
\OR\ldots\OR
f
_
n)
\OR
q
_
1
\OR
\ldots
\OR
q
_
p
\\
\F
(f
_
1
\AND\ldots\AND
f
_
n
\AND
q
_
1
\AND
\ldots
\AND
q
_
p)
&
\equivEU
\F
(f
_
1
\AND\ldots\AND
f
_
n)
\AND
q
_
1
\AND
\ldots
\AND
q
_
p
\\
\G
(f
_
1
\AND\ldots\AND
f
_
n
\AND
q
_
1
\AND
\ldots
\AND
q
_
p)
&
\equivEU
\G
(f
_
1
\AND\ldots\AND
f
_
n)
\AND
q
_
1
\AND
\ldots
\AND
q
_
p
\\
...
...
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