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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> 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 <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font> holds <br/><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font></span><br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</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="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font> implies <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font> )</span><br/>



<b>assume </b><a NAME="E1:40"/>
( <font color="Maroon" title="c1">R</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <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="c2">a</font>,<font color="Maroon" title="c3">b</font> &amp; <font color="Maroon" title="c1">R</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <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="c3">b</font>,<font color="Maroon" title="c4">c</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D4" target="_self" title="REWRITE1:def.4">REWRITE1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font></span><br/>

<b>hence </b><a NAME="E2:40"/>
<font color="Maroon" title="c1">R</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">R</font> <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="c2">a</font>,<font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="ref" href="rewrite1.html#T17" target="_self" title="REWRITE1:th.17">Th17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D4" target="_self" title="REWRITE1:def.4">REWRITE1:def 4</a> <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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