<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">S</font> =  <a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font>;<br/>
<b>set </b><font color="Maroon">g1</font> = <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font>;<br/>
<b>set </b><font color="Maroon">g2</font> = <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font>;<br/>
<b>set </b><font color="Maroon">SORTS</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">CHARACT</font> = the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">f</font>;<br/>
<a NAME="E1:89_1_1"/><i><font color="Green">E33</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> &amp; the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</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> &amp; the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</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> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> &amp; the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="funct_1.html#K1">.</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> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:89_1_1"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>then </b><i><font color="Green">E42</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
<font color="Maroon">Y</font>
<b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/>
<b>reconsider </b><font color="Maroon">SORTS</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font></span>)</span> as  <a href="relat_1.html#V2">V3</a>  <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E5:89_1_1"/><i><font color="Green">E43</font></i>: 
(  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</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> &amp;  <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</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> )
 
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E6:89_1_1"/><i><font color="Green">E45</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font>
 
<b>by </b><i/>;<br/>
<a NAME="E7:89_1_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E8:89_1_1"/><b>then </b>
<font color="Maroon">p</font> is    <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">pp</font> = <font color="Maroon">p</font> as    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E10:89_1_1"/>
<font color="Maroon">p</font> is    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p</font> as    <a href="finseq_2.html#M2">Element</a> of <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E12:89_1_1"/>
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font> <a href="partfun1.html#R1">tolerates</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">y</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="partfun1.html#D6">PARTFUN1:def 6</a><br/>

<b>assume </b><a NAME="E1:89_1_1_2"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:89_1_1_2"/><b>then </b>
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:89_1_1_2"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp; <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:89_1_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">y</font>
 <b>by </b><i>, , , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E13:89_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">SORTS</font>
 
<b>by </b><i><a class="ref" href="funct_4.html#T29">FUNCT_4:29</a></i>;<br/>
<a NAME="E14:89_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="pboole.html#K6">#</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a>  &amp;  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="pboole.html#K6">#</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="finseq_2.html#K3">*</a>  )
 
<b>by </b><i>, <a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E15:89_1_1"/><b>then </b><i><font color="Green">E78</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="pboole.html#K6">#</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">p'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">pp</font>
 
<b>by </b><i><a class="ref" href="grfunc_1.html#T8">GRFUNC_1:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="89_1_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:89_1_1_3"/><i><font color="Green">E107</font></i>: 
<font color="Maroon">i</font> <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="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span>
 ;<br/><a NAME="E2:89_1_1_3"/><b>then </b>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</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>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:89_1_1_3"/><b>then </b>
( <span class="p1">(<span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p2">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p2">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">p</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">pp</font> <a href="hidden.html#R1">=</a> <font color="Maroon">n</font> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">X</font> &amp; <span class="p1">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p2">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">Y</font> )
 <b>by </b><i>, , <a class="ref" href="circcomb.html#D2" target="_self">Def2</a>, , , , , <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>;<br/><b>hence </b><a NAME="E4:89_1_1_3"/>
<span class="p1">(<span class="default">the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p2">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">f</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p2">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>,<span class="p1">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p2">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/></div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">CHARACT</font> = the <a href="msualg_1.html#U1">OperSymbols</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">f</font> as    <a href="pboole.html#M3">ManySortedFunction</a> of <span class="p1">(<span class="default"><font color="Maroon">SORTS</font> <a href="pboole.html#K6">#</a> </span>)</span> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U2">Arity</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span>,<font color="Maroon">SORTS</font> <a href="pboole.html#K7">*</a> the <a href="msualg_1.html#U3">ResultSort</a> of <span class="p1">(<span class="default"><a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font></span>)</span> <b>by </b><i><a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/>
<b>reconsider </b><font color="Maroon">A</font> =  <a href="msualg_1.html#G3">MSAlgebra</a>(# <font color="Maroon">SORTS</font>,<font color="Maroon">CHARACT</font> #) as  <a href="msualg_1.html#V4">strict</a> <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of  <a href="circcomb.html#K6" target="_self">1GateCircStr</a> <font color="Maroon">p</font>,<font color="Maroon">f</font>,<font color="Maroon">x</font> <b>by </b><i><a class="ref" href="msualg_1.html#D8">MSUALG_1:def 8</a></i>;<br/>
<b>take </b>
<font color="Maroon">A</font>
;<br/>

<a NAME="E19:89_1_1"/>
<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#R2">in</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>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E20:89_1_1"/>
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">p</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font></span>)</span> <a href="circcomb.html#K1" target="_self">+*</a> <span class="p1">(<span class="default"><span class="p2"><a href="tarski.html#K1">{</a><span class="default"><font color="Maroon">x</font></span><a href="tarski.html#K1">}</a></span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">Y</font></span>)</span> &amp; the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</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> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> )
 <b>by </b><i>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>


</div>
