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

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <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="c1">S</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  implies (  not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:80_4_1"/><span class="lab"><font color="Green" title="E10">Z</font></span>: 
<font color="Maroon" title="c1">S</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; <font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  )</span><br/>

<span class="kw">hence </span><a NAME="E2:80_4_1"/>
 not  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="struct_0.html#D1" target="_self" title="STRUCT_0:def.1">STRUCT_0:def 1</a> <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="c1">S</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> </span><br/>

<a NAME="E3:80_4_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:80_4_1"><span class="lab"><font color="Green" title="E10">Z</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:80_4_1"/>
<font color="Maroon" title="c1">S</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 ; <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>
