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<b>let </b><font color="Maroon">A</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be    <a href="catalg_1.html#M1" target="_self">CatSignature</a> of <font color="Maroon">A</font>;<br/>



<a NAME="E1:52"/>
 <a href="catalg_1.html#K3" target="_self">CatSign</a> <font color="Maroon">A</font> is    <a href="instalg1.html#M1">Subsignature</a> of <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:52"/><b>then </b><i><font color="Green">E37</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> <font color="Maroon">A</font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font> )
 
<b>by </b><i><a class="ref" href="instalg1.html#T11">INSTALG1:11</a></i>;<br/>
<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/>

<a NAME="E3:52"/>
<span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a> 1 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:52"/><b>then </b><i><font color="Green">E41</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">1 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">1</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">1 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T128">ZFMISC_1:128</a></i>;<br/>
<a NAME="E5:52"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> <font color="Maroon">A</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E6:52"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default">1,<span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Maroon">a</font></span><a href="finseq_1.html#K12">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E7:52"/>
 <a href="catalg_1.html#K5" target="_self">idsym</a> <font color="Maroon">a</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 ;<br/>

<b>let </b><font color="Maroon">b</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/>

<a NAME="E8:52"/>
<span class="p1"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span> <a href="hidden.html#R2">in</a> 2 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E9:52"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">2 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">2 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T128">ZFMISC_1:128</a></i>;<br/>
<a NAME="E10:52"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,<span class="p2"><a href="finseq_4.html#K2">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font></span><a href="finseq_4.html#K2">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E11:52"/>
 <a href="catalg_1.html#K6" target="_self">homsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ;<br/>

<b>let </b><font color="Maroon">c</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">A</font>;<br/>

<a NAME="E12:52"/>
<span class="p1"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="finseq_4.html#K3">*&gt;</a></span> <a href="hidden.html#R2">in</a> 3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font>
 
<b>by </b><i/>;<br/>
<a NAME="E13:52"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default">2,<span class="p2"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default">2</span><a href="tarski.html#K1">}</a></span>,<span class="p2">(<span class="default">3 <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">A</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T128">ZFMISC_1:128</a></i>;<br/>
<a NAME="E14:52"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default">2,<span class="p2"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="catalg_1.html#K3" target="_self">CatSign</a> <font color="Maroon">A</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>
<a NAME="E15:52"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default">2,<span class="p2"><a href="finseq_4.html#K3">&lt;*</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font></span><a href="finseq_4.html#K3">*&gt;</a></span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E16:52"/>
 <a href="catalg_1.html#K7" target="_self">compsym</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> the <a href="msualg_1.html#U1">OperSymbols</a> of <font color="Maroon">S</font>
 ;<br/>


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