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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">Q</font> being <a href="rewrite1.html#V10" title="REWRITE1:attr.10">complete</a> <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>  st <font color="Maroon" title="c1">R</font>,<font color="Olive" title="b1">Q</font> <a href="rewrite1.html#R12" title="REWRITE1:pred.12">are_equivalent</a>  holds <br/><font color="Olive" title="b1">Q</font> is    <a href="rewrite1.html#M2" title="REWRITE1:mode.2">Completion</a> of <font color="Maroon" title="c1">R</font></span><br/><b>let </b><font color="Maroon" title="c2">Q</font> be  <a href="rewrite1.html#V10" title="REWRITE1:attr.10">complete</a> <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"> ( <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">Q</font> <a href="rewrite1.html#R12" title="REWRITE1:pred.12">are_equivalent</a>  implies <font color="Maroon" title="c2">Q</font> is    <a href="rewrite1.html#M2" title="REWRITE1:mode.2">Completion</a> of <font color="Maroon" title="c1">R</font> )</span><br/>



<b>assume </b><a NAME="E1:94"/><i><font color="Green" title="E70">A1</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <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> iff <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="c2">Q</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D26" target="_self" title="REWRITE1:def.26">REWRITE1:def 26</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">Q</font> is    <a href="rewrite1.html#M2" title="REWRITE1:mode.2">Completion</a> of <font color="Maroon" title="c1">R</font></span><br/>

<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D28" target="_self" title="REWRITE1:def.28">REWRITE1:def 28</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font> iff <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a> <font color="Maroon" title="c2">Q</font> )</span><br/>

<a NAME="E2:94"/>
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font> iff <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c2">Q</font> )
 
<b>by </b><i><a class="txt" href="#E1:94"><i><font color="Green" title="E70">A1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:94"/>
( <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c1">R</font> iff <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> <a href="rewrite1.html#R5" title="REWRITE1:pred.5">are_convergent_wrt</a> <font color="Maroon" title="c2">Q</font> )
 <b>by </b><i><a class="ref" href="rewrite1.html#D23" target="_self" title="REWRITE1:def.23">Def23</a>, <a class="ref" href="rewrite1.html#T38" target="_self" title="REWRITE1:th.38">Th38</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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