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<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D16">PBOOLE:def 16</a><br/>

<b>assume </b><a NAME="E1:10_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<a NAME="E2:10_1_1"/><b>then </b><i><font color="Green">E40</font></i>: 
 ex <font color="Olive">R</font> being   <a href="struct_0.html#L1">1-sorted</a>  st <br/>( <font color="Olive">R</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> &amp; <span class="p1">(<span class="default"><a href="pralg_1.html#K12">Carrier</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> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">R</font> )
 
<b>by </b><i><a class="ref" href="pralg_1.html#D13">PRALG_1:def 13</a></i>;<br/>
<a NAME="E3:10_1_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <font color="Maroon">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E4:10_1_1"/><b>then </b>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">F</font>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E5:10_1_1"/><b>then </b>
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is  non <a href="struct_0.html#V3">empty</a>  <a href="group_1.html#L1">HGrStr</a> 
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:10_1_1"/>
not <span class="p1">(<span class="default"><a href="pralg_1.html#K12">Carrier</a> <font color="Maroon">F</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i>, <a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/>


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