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<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="rewrite1.html#V4" title="REWRITE1:attr.4">with_UN_property</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"> 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="b2">b</font> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c1">R</font> &amp; <font color="Olive" title="b3">c</font> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Olive" title="b1">a</font>,<font color="Maroon" title="c1">R</font> holds <br/><font color="Olive" title="b2">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">c</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="c3">b</font> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c4">c</font> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font> implies <font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font> )</span><br/>



<b>assume </b><b>that </b><br/><a NAME="E1:76"/><i><font color="Green" title="E64">A1</font></i>: 
( <font color="Maroon" title="c3">b</font> <a href="rewrite1.html#R3" title="REWRITE1:pred.3">is_a_normal_form_wrt</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c1">R</font> <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> )
 <b>and </b><br/><a NAME="E2:76"/><i><font color="Green" title="E65">A2</font></i>: 
( <font color="Maroon" title="c4">c</font> <a href="rewrite1.html#R3" title="REWRITE1:pred.3">is_a_normal_form_wrt</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c1">R</font> <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> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="rewrite1.html#D6" target="_self" title="REWRITE1:def.6">REWRITE1:def 6</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">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font></span><br/>

<a NAME="E3:76"/>
<font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="rewrite1.html#R6" title="REWRITE1:pred.6">are_divergent_wrt</a> <font color="Maroon" title="c1">R</font>
 
<b>by </b><i><a class="txt" href="#E1:76"><i><font color="Green" title="E64">A1</font></i></a>, <a class="txt" href="#E2:76"><i><font color="Green" title="E65">A2</font></i></a>, <a class="ref" href="rewrite1.html#D8" target="_self" title="REWRITE1:def.8">Def8</a></i>;<br/>
<a NAME="E4:76"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="rewrite1.html#T38" target="_self" title="REWRITE1:th.38">Th38</a></i>;<br/>
<b>hence </b><a NAME="E5:76"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">c</font>
 <b>by </b><i><a class="txt" href="#E1:76"><i><font color="Green" title="E64">A1</font></i></a>, <a class="txt" href="#E2:76"><i><font color="Green" title="E65">A2</font></i></a>, <a class="ref" href="rewrite1.html#D19" target="_self" title="REWRITE1:def.19">Def19</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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