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<span class="kw">let </span><font color="Maroon" title="c1">GS</font> be   <a href="glib_000.html#NM11" title="GLIB_000:NM.11">GraphSeq</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">GS</font> is  <a href="glib_000.html#V16" title="GLIB_000:attr.16">trivial</a>  &amp; <font color="Maroon" title="c1">GS</font> is  <a href="glib_000.html#V15" title="GLIB_000:attr.15">loopless</a>  implies <font color="Maroon" title="c1">GS</font> is  <a href="glib_000.html#V14" title="GLIB_000:attr.14">finite</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:109_1_1"/>
( <font color="Maroon" title="c1">GS</font> is  <a href="glib_000.html#V16" title="GLIB_000:attr.16">trivial</a>  &amp; <font color="Maroon" title="c1">GS</font> is  <a href="glib_000.html#V15" title="GLIB_000:attr.15">loopless</a>  )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">GS</font> is  <a href="glib_000.html#V14" title="GLIB_000:attr.14">finite</a> </span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">GS9</font> = <font color="Maroon" title="c1">GS</font> as   <a href="glib_000.html#V15" title="GLIB_000:attr.15">loopless</a>   <a href="glib_000.html#V16" title="GLIB_000:attr.16">trivial</a>  <a href="glib_000.html#NM11" title="GLIB_000:NM.11">GraphSeq</a> ;<br/>
<a NAME="E3:109_1_1"/>
 for <font color="Olive" title="b1">x</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c2">GS9</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> is  <a href="glib_000.html#V2" title="GLIB_000:attr.2">finite</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E4:109_1_1"/>
<font color="Maroon" title="c1">GS</font> is  <a href="glib_000.html#V14" title="GLIB_000:attr.14">finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D57" target="_self" title="GLIB_000:def.57">Def60</a></span>; <a class="txt" 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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