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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:59_1_1_1"/>
<font color="Maroon" title="c2">a</font> is   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font>
 ;<br/><b>then reconsider </b><font color="Maroon" title="c3">b</font> = <font color="Maroon" title="c2">a</font> as   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font> ;<br/><b>take </b><font color="Maroon" title="c4">x</font> =  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">b</font></span>)</span>;<br/><b>take </b><font color="Maroon" title="c5">b</font> = <font color="Maroon" title="c3">b</font>;<br/><b>thus </b><a NAME="E3:59_1_1_1"/>
( <font color="Maroon" title="c5">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">proj1</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c5">b</font></span>)</span> )
 ;<br/></div>
<b>end;</b></div>

<b>thus </b><a NAME="E2:59_1_1"/>
( <font color="Maroon" title="c2">a</font> is  not   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">C</font> implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 ;<br/>


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