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* doc/tl/tl.tex: Typos

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Florian Perlié-Long 2017-12-22 15:41:45 +01:00 • committed by Alexandre Duret-Lutz
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doc/tl/tl.tex
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@ -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 The following more complicated rules are generalizations of $f\AND
\X\G f\equiv \G f$ and $f\OR \X\F f\equiv \F f$: \X\G f\equiv \G f$ and $f\OR \X\F f\equiv \F f$:
\begin{align*} \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\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\ldots) &\equiv \F(f) \OR \X(h\ldots) f\OR \X(\F(f)\OR h\OR \ldots) &\equiv \F(f) \OR \X(h\OR \ldots)
\end{align*} \end{align*}
The latter rule for $f\OR \X(\F(f)\OR h\ldots)$ is only applied if all 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 $\F$-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*} \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 \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) \\ \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 \AND u_p) \\ \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 \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) \\ \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 \\ \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 \\ \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 \\ \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 \\