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<b>let </b><font color="Maroon" title="c3">R</font>, <font color="Maroon" title="c4">Q</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>;<br/>

<b>assume </b><a NAME="E1:68_1_1"/><i><font color="Green" title="E55">A1</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Q</font> holds <br/> ex <font color="Olive" title="b4">d</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c4">Q</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font> &amp; <font color="Maroon" title="c3">R</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font>, <font color="Maroon" title="c7">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E2:68_1_1"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">Q</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c7">c</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">R</font> )
 ;<br/>

<a NAME="E3:68_1_1"/><b>then </b>
 ex <font color="Olive" title="b1">d</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c4">Q</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c7">c</font>,<font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c3">R</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c6">b</font>,<font color="Olive" title="b1">d</font> )
 
<b>by </b><i><a class="txt" href="rewrite1.html#E1:68_1_1"><i><font color="Green" title="E55">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:68_1_1"/>
 ex <font color="Olive" title="b1">d</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>( <font color="Maroon" title="c3">R</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c6">b</font>,<font color="Olive" title="b1">d</font> &amp; <font color="Maroon" title="c4">Q</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c7">c</font>,<font color="Olive" title="b1">d</font> )
 ;<br/>


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