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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="115_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:115_1_1_1"/>
( <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a>  or <font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="115_1_1_1_1"><b>suppose </b></a><a NAME="E1:115_1_1_1_1"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a> 
 ;<br/><div class="add"><b>hence </b><a NAME="E2:115_1_1_1_1"/>
( ( <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a>  implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <span class="p2">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> 0</span>)</span></span>)</span> ) &amp; ( not <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a>  implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</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> &amp;  <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> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span> <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="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">n</font></span>)</span></span>)</span> ) ) )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="115_1_1_1_2"><b>suppose </b></a><a NAME="E1:115_1_1_1_2"/>
<font color="Maroon">n</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">w</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:115_1_1_1_2"/><i><font color="Green">E34</font></i>: 
not <font color="Maroon">w</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</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>
 <b>and </b><br/><a NAME="E4:115_1_1_1_2"/><i><font color="Green">E36</font></i>: 
 <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> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span> <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="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Maroon">w</font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">n</font></span>)</span></span>)</span>
 <b>by </b><i/>;<br/><b>thus </b><a NAME="E5:115_1_1_1_2"/>
( ( <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a>  implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="subset_1.html#K10">choose</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6">the_Vertices_of</a> <span class="p2">(<span class="default"><font color="Maroon">GS</font> <a href="lexbfs.html#K8" target="_self">.</a> 0</span>)</span></span>)</span> ) &amp; ( not <font color="Maroon">n</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a>  implies  ex <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</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> &amp;  <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> <span class="p2">(<span class="default"><font color="Maroon">n</font> <a href="xcmplx_0.html#K2">+</a> 1</span>)</span></span>)</span> <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="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="cqc_lang.html#K3">.--&gt;</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">GS</font> <a href="glib_000.html#K40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3">-'</a> <font color="Maroon">n</font></span>)</span></span>)</span> ) ) )
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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