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

<span class="kw">let </span><font color="Maroon" title="c3">A</font> be    <a href="circcmb3.html#M2" title="CIRCCMB3:mode.2">Circuit</a> of <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> is  <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a>  &amp; <font color="Maroon" title="c3">A</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:53_1_1"/>
<font color="Maroon" title="c3">A</font> is  <a href="circcomb.html#V4" title="CIRCCOMB:attr.4">gate`2=den</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="circcmb3.html#D10" target="_self" title="CIRCCMB3:def.10">Def10</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">A</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> </span><br/>

<a NAME="E2:53_1_1"/>
(  not  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp;  <a href="funct_1.html#K3" title="FUNCT_1:func.3">the_value_of</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="circcmb3.html#D10" target="_self" title="CIRCCMB3:def.10">Def10</a></span>;<br/>
<a NAME="E3:53_1_1"/><span class="kw">then </span>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font> &amp; (  for <font color="Olive" title="b1">i</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a>  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font> holds <br/> not  the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#D12" title="FUNCT_1:def.12">FUNCT_1:def 12</a>, <a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a></span>;<br/>
<a NAME="E4:53_1_1"/><span class="kw">then </span>
 the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c3">A</font> is  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#D13" title="PBOOLE:def.13">PBOOLE:def 13</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:53_1_1"/>
<font color="Maroon" title="c3">A</font> is  <a href="msualg_1.html#V4" title="MSUALG_1:attr.4">non-empty</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_1.html#D3" title="MSUALG_1:def.3">MSUALG_1:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
