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<span class="kw">let </span><font color="Maroon" title="c1">GSq</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">GSq</font> is  <a href="glib_002.html#V7" title="GLIB_002:attr.7">acyclic</a>  implies <font color="Maroon" title="c1">GSq</font> is  <a href="glib_000.html#V20" title="GLIB_000:attr.20">simple</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:56_3_1"/><span class="lab"><font color="Green" title="E39">A3</font></span>: 
<font color="Maroon" title="c1">GSq</font> is  <a href="glib_002.html#V7" title="GLIB_002:attr.7">acyclic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">GSq</font> is  <a href="glib_000.html#V20" title="GLIB_000:attr.20">simple</a> </span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_3_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c2">n</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> </span><br/><span class="kw">reconsider </span><font color="Maroon" title="c3">G</font> = <font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c2">n</font> as   <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:56_3_1"><span class="lab"><font color="Green" title="E39">A3</font></span></a>, <a class="ref" href="glib_002.html#D13" target="_self" title="GLIB_002:def.13">Def13</a></span>;<br/><a NAME="E2:56_3_1_1"/>
<font color="Maroon" title="c3">G</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> 
 ;<br/><span class="kw">hence </span><a NAME="E3:56_3_1_1"/>
<font color="Maroon" title="c1">GSq</font> <a href="glib_000.html#K41" title="GLIB_000:func.41">.</a> <font color="Maroon" title="c2">n</font> is  <a href="glib_000.html#V7" title="GLIB_000:attr.7">simple</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:56_3_1"/>
<font color="Maroon" title="c1">GSq</font> is  <a href="glib_000.html#V20" title="GLIB_000:attr.20">simple</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D66" title="GLIB_000:def.66">GLIB_000:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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