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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">R</font> being   <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">R</font> is  <a href="rewrite1.html#V4" title="REWRITE1:attr.4">with_UN_property</a>  &amp; <font color="Olive" title="b1">R</font> is  <a href="rewrite1.html#V2" title="REWRITE1:attr.2">weakly-normalizing</a>  holds <br/> for <font color="Olive" title="b2">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> holds   <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> (<font color="Olive" title="b2">x</font>,<font color="Olive" title="b1">R</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font> be   <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">R</font> is  <a href="rewrite1.html#V4" title="REWRITE1:attr.4">with_UN_property</a>  &amp; <font color="Maroon" title="c2">R</font> is  <a href="rewrite1.html#V2" title="REWRITE1:attr.2">weakly-normalizing</a>  implies  for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> holds   <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">R</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:120"/><span class="lab"><font color="Green" title="E70">A1</font></span>: 
( <font color="Maroon" title="c2">R</font> is  <a href="rewrite1.html#V4" title="REWRITE1:attr.4">with_UN_property</a>  &amp; <font color="Maroon" title="c2">R</font> is  <a href="rewrite1.html#V2" title="REWRITE1:attr.2">weakly-normalizing</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> holds   <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> (<font color="Olive" title="b1">x</font>,<font color="Maroon" title="c2">R</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">R</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font></span><br/>

<a NAME="E2:120"/>
 <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">R</font>) <a href="rewrite1.html#R4" title="REWRITE1:pred.4">is_a_normal_form_of</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:120"><span class="lab"><font color="Green" title="E70">A1</font></span></a>, <a class="ref" href="rewrite1.html#T54" onmouseover="rs('rewrite1/T54')" onmouseout="rh()">REWRITE1:54</a></span>;<br/>
<a NAME="E3:120"/><span class="kw">then </span>
<font color="Maroon" title="c2">R</font> <a href="rewrite1.html#R1" title="REWRITE1:pred.1">reduces</a> <font color="Maroon" title="c3">x</font>, <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">R</font>)
 
;<br/>
<span class="kw">hence </span><a NAME="E4:120"/>
 <a href="rewrite1.html#K2" title="REWRITE1:func.2">nf</a> (<font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c2">R</font>) <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="abcmiz_0.html#T74" target="_self" onmouseover="rs('abcmiz_0/T74')" onmouseout="rh()">Th74</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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