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<b>let </b><font color="Maroon" title="c1">R</font> be  <a href="rewrite1.html#V2" title="REWRITE1:attr.2">weakly-normalizing</a> <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>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<a NAME="E1:81"/><i><font color="Green" title="E66">A1</font></i>: 
(  <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</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;  <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">R</font> <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">R</font> )
 
<b>by </b><i><a class="ref" href="rewrite1.html#T55" target="_self" title="REWRITE1:th.55">Th55</a></i>;<br/>
<a NAME="E2:81"/><b>then </b><i><font color="Green" title="E67">A2</font></i>: 
(  <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font> <a href="rewrite1.html#R3" title="REWRITE1:pred.3">is_a_normal_form_wrt</a> <font color="Maroon" title="c1">R</font> &amp;  <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">R</font> <a href="rewrite1.html#R3" title="REWRITE1:pred.3">is_a_normal_form_wrt</a> <font color="Maroon" title="c1">R</font> )
 
<b>by </b><i><a class="ref" href="rewrite1.html#D6" target="_self" title="REWRITE1:def.6">Def6</a></i>;<br/>
<a NAME="E3:81"/>
( <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>, <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c2">a</font>,<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="c3">b</font>, <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">R</font> )
 
<b>by </b><i><a class="txt" href="rewrite1.html#E1:81"><i><font color="Green" title="E66">A1</font></i></a>, <a class="ref" href="rewrite1.html#D6" target="_self" title="REWRITE1:def.6">Def6</a></i>;<br/>
<a NAME="E4:81"/><b>then </b><i><font color="Green" title="E68">A3</font></i>: 
(  <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">a</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>, <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">R</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#T26" target="_self" title="REWRITE1:th.26">Th26</a></i>;<br/>
<b>assume </b><a NAME="E5:81"/>
<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>
 ;<br/>

<a NAME="E6:81"/><b>then </b>
 <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</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>
 
<b>by </b><i><a class="txt" href="rewrite1.html#E4:81"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="rewrite1.html#T31" target="_self" title="REWRITE1:th.31">Th31</a></i>;<br/>
<a NAME="E7:81"/><b>then </b>
 <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font>, <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">R</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="txt" href="rewrite1.html#E4:81"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="rewrite1.html#T31" target="_self" title="REWRITE1:th.31">Th31</a></i>;<br/>
<b>hence </b><a NAME="E8:81"/>
 <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c1">R</font>
 <b>by </b><i><a class="txt" href="rewrite1.html#E2:81"><i><font color="Green" title="E67">A2</font></i></a>, <a class="ref" href="rewrite1.html#D19" target="_self" title="REWRITE1:def.19">Def19</a></i>;<br/>


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