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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:91_1_1_1"/>
<font color="Maroon" title="c1">GSq</font> is <a href="glib_000.html#V13" title="GLIB_000:attr.13">halting</a>
 ;<br/><b>then consider </b><font color="Maroon" title="c2">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E3:91_1_1_1"/><i><font color="Green" title="E46">A1</font></i>: 
<font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K42" title="GLIB_000:func.42">.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K42" title="GLIB_000:func.42">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="ref" href="glib_000.html#D56" target="_self" title="GLIB_000:def.56">Def56</a></i>;<br/><b>thus </b><a NAME="E4:91_1_1_1"/>
 ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K42" title="GLIB_000:func.42">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K42" title="GLIB_000:func.42">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <b>by </b><i><a class="txt" href="glib_000.html#E3:91_1_1_1"><i><font color="Green" title="E46">A1</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:91_1_1"/>
 ex <font color="Olive" title="b1">n</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> st <font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K42" title="GLIB_000:func.42">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K42" title="GLIB_000:func.42">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c2">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E4:91_1_1"/><i><font color="Green" title="E46">A2</font></i>: 
<font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K42" title="GLIB_000:func.42">.</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K42" title="GLIB_000:func.42">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">n</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 ;<br/>
<b>thus </b><a NAME="E5:91_1_1"/>
<font color="Maroon" title="c1">GSq</font> is <a href="glib_000.html#V13" title="GLIB_000:attr.13">halting</a>
 <b>by </b><i><a class="txt" href="glib_000.html#E4:91_1_1"><i><font color="Green" title="E46">A2</font></i></a>, <a class="ref" href="glib_000.html#D56" target="_self" title="GLIB_000:def.56">Def56</a></i>;<br/>


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