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<b>let </b><font color="Maroon">x</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="E1:26_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 ;<br/>

<b>then consider </b><font color="Maroon">U0</font> being    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font><b> such that </b><br/><a NAME="E3:26_1_1"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">U0</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> &amp; <span class="p1">(<span class="default"><a href="pralg_2.html#K10" target="_self">Carrier</a> <font color="Maroon">A</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s</font> )
 <b>by </b><i/>;<br/>
<a NAME="E4:26_1_1"/>
<font color="Maroon">U0</font> is  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:26_1_1"/><b>then </b>
the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">U0</font> is <a href="relat_1.html#V2">non-empty</a>
 
<b>by </b><i><a class="ref" href="msualg_1.html#D8">MSUALG_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E6:26_1_1"/>
not <span class="p1">(<span class="default"><a href="pralg_2.html#K10" target="_self">Carrier</a> <font color="Maroon">A</font>,<font color="Maroon">s</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> is <a href="xboole_0.html#V1">empty</a>
 <b>by </b><i>, <a class="ref" href="pboole.html#D16">PBOOLE:def 16</a></i>;<br/>


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