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<b>let </b><font color="Maroon">s</font> be   <a href="circuit1.html#NM3">State</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K7" target="_self">1GateCircuit</a> <span class="p2"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span>;<br/><b>let </b><font color="Maroon">a1</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>4</sub></font>(), <font color="Maroon">a2</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>4</sub></font>(), <font color="Maroon">a3</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>4</sub></font>();<br/>



<b>assume </b><a NAME="E1:79_1"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">a1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">a2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon">a3</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>() )
 ;<br/>

<b>set </b><font color="Maroon">S</font> =  <a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <span class="p1"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>();<br/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> = 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <span class="p2"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span>
<b>by </b><i><a class="ref" href="circuit1.html#T4">CIRCUIT1:4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span></span>)</span> <a href="xboole_0.html#K2">\/</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"><span class="p3"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></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="circcomb.html#D6">CIRCCOMB:def 6</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="enumset1.html#K1">}</a></span> <a href="xboole_0.html#K2">\/</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"><span class="p3"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></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="finseq_2.html#T148">FINSEQ_2:148</a></i>
<br/>.= 
<span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>(),<span class="p2"><a href="tarski.html#K4">[</a><span class="default"><span class="p3"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4">]</a></span></span><a href="enumset1.html#K2">}</a></span>
<b>by </b><i><a class="ref" href="enumset1.html#T46">ENUMSET1:46</a></i>
;<br/>
<a NAME="E3:79_1"/><b>then </b>
( <font color="Maroon">F<sub>1</sub></font>() <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> &amp; <font color="Maroon">F<sub>2</sub></font>() <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> &amp; <font color="Maroon">F<sub>3</sub></font>() <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">s</font> )
 
<b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/>
<a NAME="E4:79_1"/><b>then </b><i><font color="Green">E37</font></i>: 
<font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a3</font></span><a href="facirc_1.html#K7">*&gt;</a></span>
 
<b>by </b><i>, <a class="ref" href="finseq_2.html#T146">FINSEQ_2:146</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="circcmb3.html#K1" target="_self">Result</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K5" target="_self">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="circcmb3.html#K5" target="_self">Output</a> <span class="p2">(<span class="default"><a href="circcmb3.html#K6" target="_self">1GateCircStr</a> <span class="p3"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="circuit2.html#K6">Following</a> <font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span>,<font color="Maroon">F<sub>6</sub></font>()</span><a href="tarski.html#K4">]</a></span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F<sub>6</sub></font>() <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">s</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2"><a href="facirc_1.html#K7">&lt;*</a><span class="default"><font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>()</span><a href="facirc_1.html#K7">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="circcomb.html#T64">CIRCCOMB:64</a></i>
<br/>.= 
<font color="Maroon">F<sub>5</sub></font>(<font color="Maroon">a1</font>,<font color="Maroon">a2</font>,<font color="Maroon">a3</font>)
<b>by </b><i><a class="txt" href="circcmb3.html#E4:79_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="circcmb3.html#D1" target="_self">Def1</a></i>
;<br/>


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