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<b>consider </b><font color="Maroon" title="c1">A</font> being  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>
<b>take </b><font color="Maroon" title="c2">S</font> =  <a href="catalg_1.html#K2" title="CATALG_1:func.2">CatSign</a> <font color="Maroon" title="c1">A</font>;<br/>

<b>thus </b><a NAME="E2:28_1_1"/>
<font color="Maroon" title="c2">S</font> is <a href="catalg_1.html#V2" title="CATALG_1:attr.2">Categorial</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1_1_1"><b>proof </b></a><div class="add">

<b>take </b>
<font color="Maroon" title="c1">A</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="catalg_1.html#D6" target="_self" title="CATALG_1:def.6">CATALG_1:def 6</a><br/>

<b>thus </b><a NAME="E1:28_1_1_1"/>
(  <a href="catalg_1.html#K2" title="CATALG_1:func.2">CatSign</a> <font color="Maroon" title="c1">A</font> is    <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c2">S</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">0</span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>,<span class="p2">(<span class="default">2 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <font color="Maroon" title="c1">A</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 <b>by </b><i><a class="ref" href="catalg_1.html#D5" target="_self" title="CATALG_1:def.5">Def5</a>, <a class="ref" href="instalg1.html#T16" title="INSTALG1:th.16">INSTALG1:16</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E3:28_1_1"/>
( not <font color="Maroon" title="c2">S</font> is <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> &amp; <font color="Maroon" title="c2">S</font> is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> )
 ;<br/>


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