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<b>let </b><font color="Maroon" title="c1">a</font>, <font color="Maroon" title="c2">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  implies <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font> )</span><br/>

<b>assume </b><a NAME="E1:37"/>
<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font></span><br/>

<a NAME="E2:37"/><b>then </b>
( <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a> </span>)</span> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c2">b</font> &amp;  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  )
 
<b>by </b><i><a class="ref" href="rewrite1.html#D4" target="_self" title="REWRITE1:def.4">Def4</a></i>;<br/>
<b>hence </b><a NAME="E3:37"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">b</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T14" target="_self" title="REWRITE1:th.14">Th14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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