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

<b>let </b><font color="Maroon">X</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S1</font> be    <a href="circcmb3.html#M1" target="_self">Signature</a> of <font color="Maroon">X</font>, <font color="Maroon">S2</font> be    <a href="circcmb3.html#M1" target="_self">Signature</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">A1</font> be    <a href="circcmb3.html#M2" target="_self">Circuit</a> of <font color="Maroon">X</font>,<font color="Maroon">S1</font>;<br/><b>let </b><font color="Maroon">A2</font> be    <a href="circcmb3.html#M2" target="_self">Circuit</a> of <font color="Maroon">X</font>,<font color="Maroon">S2</font>;<br/>







<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">A1</font> <a href="circcomb.html#K4">+*</a> <font color="Maroon">A2</font> as   <a href="circuit1.html#NM1">Circuit</a> of <font color="Maroon">S1</font> <a href="circcomb.html#K3">+*</a> <font color="Maroon">S2</font> <b>by </b><i/>;<br/>
<a NAME="E2:63"/>
<font color="Maroon">A1</font> <a href="circcomb.html#R2">tolerates</a> <font color="Maroon">A2</font>
 
<b>by </b><i><a class="ref" href="circcmb3.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E3:63"/><b>then </b><i><font color="Green">E34</font></i>: 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="partfun1.html#R1">tolerates</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font>
 
<b>by </b><i><a class="ref" href="circcomb.html#D3">CIRCCOMB:def 3</a></i>;<br/>
<a NAME="E4:63"/>
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> is <a href="funct_1.html#V3">constant</a> &amp;  <a href="yellow_6.html#K1">the_value_of</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> is <a href="funct_1.html#V3">constant</a> &amp;  <a href="yellow_6.html#K1">the_value_of</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:63"/><b>then </b>
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E6:63"/><b>then </b><i><font color="Green">E36</font></i>: 
( the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font></span>)</span>,<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></span><a href="zfmisc_1.html#K2">:]</a></span> &amp; the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font></span>)</span>,<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></span><a href="zfmisc_1.html#K2">:]</a></span> )
 
<b>by </b><i><a class="ref" href="funcop_1.html#D2">FUNCOP_1:def 2</a></i>;<br/>
<a NAME="E7:63"/><i><font color="Green">E37</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> = 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="circcomb.html#K1">+*</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font>
<b>by </b><i>, <a class="ref" href="circcomb.html#D4">CIRCCOMB:def 4</a></i>
<br/>.= 
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font> <a href="xboole_0.html#K2">\/</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font>
<b>by </b><i>, <a class="ref" href="funct_4.html#T31">FUNCT_4:31</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font></span>)</span></span>)</span>,<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></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T120">ZFMISC_1:120</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="xboole_0.html#K2">\/</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font></span>)</span></span>)</span> <a href="pre_circ.html#K2">--&gt;</a> <font color="Maroon">X</font>
<b>by </b><i><a class="txt" href="circcmb3.html#E3:63"><i><font color="Green">E34</font></i></a>, <a class="ref" href="funcop_1.html#D2">FUNCOP_1:def 2</a></i>
;<br/>
<b>hence </b><a NAME="E9:63"/>
( the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="circcomb.html#K4">+*</a> <font color="Maroon">A2</font></span>)</span> is <a href="funct_1.html#V3">constant</a> &amp;  <a href="yellow_6.html#K1">the_value_of</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<span class="default"><font color="Maroon">A1</font> <a href="circcomb.html#K4">+*</a> <font color="Maroon">A2</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> )
 <b>by </b><i><a class="ref" href="yellow_6.html#T2">YELLOW_6:2</a></i>;<br/>


</div>
