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<b>let </b><font color="Maroon">GS</font> be   <a href="lexbfs.html#NM10">VLabelNumberingSeq</a>;<br/><b>let </b><font color="Maroon">m</font> be   <a href="nat_1.html#NM1">Nat</a>, <font color="Maroon">n</font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">v</font> be    <a href="hidden.html#M1">set</a> ;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:124"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">m</font></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 <b>and </b><br/><a NAME="E2:124"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">v</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="glib_003.html#K14">.labeledV()</a> 
 ;<br/>

<b>set </b><font color="Maroon">VLM</font> =  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">m</font></span>)</span>;<br/>
<b>set </b><font color="Maroon">VLN</font> =  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">n</font></span>)</span>;<br/>
<a NAME="E3:124"/><i><font color="Green">E38</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">v</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">v</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">m</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>;<br/>
<a NAME="E4:124"/><i><font color="Green">E39</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">v</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p4">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">v</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">n</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lexbfs.html#T2" target="_self">Th2</a>, <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="124_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:124_1"/>
( <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font> or <font color="Maroon">m</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">n</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="124_1_1"><b>suppose </b></a><a NAME="E1:124_1_1"/>
<font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 ;<br/><div class="add"><a NAME="E2:124_1_1"/><b>then </b>
 <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">m</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E2"><i><font color="Green">Lemma52</font></i></a></i>;<br/><b>hence </b><a NAME="E3:124_1_1"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">v</font>
 <b>by </b><i><a class="ref" href="lexbfs.html#T2" target="_self">Th2</a>, , <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="124_1_2"><b>suppose </b></a><a NAME="E1:124_1_2"/>
<font color="Maroon">m</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> <font color="Maroon">n</font>
 ;<br/><div class="add"><a NAME="E2:124_1_2"/><b>then </b>
 <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">n</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="glib_003.html#K7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">m</font></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E2"><i><font color="Green">Lemma52</font></i></a></i>;<br/><b>hence </b><a NAME="E3:124_1_2"/>
<span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">m</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> <font color="Maroon">n</font></span>)</span></span>)</span> <a href="polynom1.html#K8">.</a> <font color="Maroon">v</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#D4">FUNCT_1:def 4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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