🚀 go-pugleaf

$B!tLu$"$C$F!"0lC6<h$j2<$2!":FEj9F$7$^$7$?!#(B

>>   $BLdBj$NN}=,LdBjJ8$N0lIt(B(hint$B$r=|$$$?$@$1(B)$B$O0J2<$G$9!#(B
>>   $B!V(BShow that every proper initial segment of a restricted formula has
>> more left than right parentheses.$B!W(B
>
>$B$3$NLdBjJ8$+$i$9$k$H!"(Bproper subset $B$N(B Proper $B$G$h$$$N$G$O$J$$$G$7$g$&$+!#(B

$B$=$N$h$&$G$9$M!#(B $B<:Ni$7$^$7$?!#(B
$BDL>o$N?t<0$G$O!"3g8L$H$$$&$b$N$O$D$1$J$$$HB?5A@-$,@8$:$k;~$K$N$_(B
$B$D$1$k$o$1$G$9$,!"$3$3$G$O1i;;;R$NF/$/(B2$B9`$rL@<(E*$K<($9$?$a$K!"I,$:(B
$B3g8L$r;H$&$3$H$K$7$F$$$k$o$1$G$9!#$7$?$,$C$F!"85$N<0$N:G8e$OI,$:JD$8(B
$B3g8L$G=*$k$N$G(B more left than right$B$K$J$k!"$H$$$&$3$H$K$J$j$^$9!#(B

>  1. <atomic>
>  2. $BH]Dj5-9f(B<$BL?BjO@M}<0(B>
>  3. (<$BL?BjO@M}<0(B> @ <$BL?BjO@M}<0(B>)
>     $B!V(B@$B!W$O(Bbinary operator$B$G$9!#Hs=*C<5-9f$r0O$`$N$K(B<>$B$r;H$$$^$7$?!#(B

>  a restricted formula$B$O!">e$+$i(B 2 $B$r=|$$$?(B($BH]Dj5-9f$r4^$^$J$$(B)$B<0$G$9!#(B

restrict $B$7$J$$$H$-$NNc30$O!"H]Dj5-9f(B1$B8D0J>e(B<atomic>$B$N>l9g$@$1$G$9!#(B
atomic $B$N8D?t$K4X$9$k5"G<K!$rMQ$$$k$N$,>oF;$G$9!#(B

>#   TeX$B$OCN$i$J$$$N$G!"$3$N5-;v$K(Bfollow$B$9$k$J$i!"(BTeX$B$N5-K!$r;H$o$J$$$h(B
># $B$&4uK>$7$^$9!#(B

$BO@M}$K<h$jAH$^$l$F$$$kJ}$J$i3Z$KF~$C$F$$$1$k$H;W$$$^$9$,!#(B
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        $BJ!(B  $BEg(B  $B0KCNO:(B
        ichiro@ms.u-tokyo.ac.jp,nn66040@hongo.ecc.u-tokyo.ac.jp
        $BEl5~Bg3XBg3X1!(B $B?tM}2J3X8&5f2J?tM}2J3X@l96(B $B=$;N2]Dx(B
	$B6M0~3X1`9bEy3X9;(B/$BBg:J9bEy3X9;$[$+Hs>o6P9V;U(B