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<b>let </b><font color="Maroon">f</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="finseq_1.html#NM1">FinSequence</a>, <font color="Maroon">q</font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<b>set </b><font color="Maroon">S1</font> =  <a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>;<br/>
<b>set </b><font color="Maroon">S2</font> =  <a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">q</font>,<font color="Maroon">f</font>;<br/>
<a NAME="E1:68"/><i><font color="Green">E24</font></i>: 
( the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">p</font> &amp; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">q</font>,<font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">q</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:68"/><i><font color="Green">E33</font></i>: 
( the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">q</font>,<font color="Maroon">f</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:68"/><i><font color="Green">E38</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span> implies <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">p</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> <a href="subset_1.html#R1">misses</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">q</font>,<font color="Maroon">f</font></span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K1">}</a></span> )
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T17">ZFMISC_1:17</a></i>;<br/>
<b>hence </b><a NAME="E4:68"/>
the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">q</font>,<font color="Maroon">f</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D1" target="_self">CIRCCOMB:def 1</a><br/>

<b>thus </b><a NAME="E5:68"/>
the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font></span>)</span> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K7" target="_self">1GateCircStr</a> <font color="Maroon">q</font>,<font color="Maroon">f</font></span>)</span>
 <b>by </b><i>, , </i>;<br/>


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