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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="glib_014.html#V1" title="GLIB_014:attr.1">Graph-membered</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">S</font> is  <a href="glpacy00.html#V6" title="GLPACY00:attr.6">Cycle-like</a>  implies <font color="Maroon" title="c1">S</font> is  <a href="glib_014.html#V9" title="GLIB_014:attr.9">connected</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:83_2_1"/><span class="lab"><font color="Green" title="E45">A1</font></span>: 
<font color="Maroon" title="c1">S</font> is  <a href="glpacy00.html#V6" title="GLPACY00:attr.6">Cycle-like</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">S</font> is  <a href="glib_014.html#V9" title="GLIB_014:attr.9">connected</a> </span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="83_2_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">G</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>  st <font color="Olive" title="b1">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font> holds <br/><font color="Olive" title="b1">G</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">G</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font> implies <font color="Maroon" title="c2">G</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a>  )</span><br/><span class="kw">assume </span><a NAME="E1:83_2_1_1"/>
<font color="Maroon" title="c2">G</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">G</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> </span><br/><a NAME="E2:83_2_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">G</font> is  <a href="glpacy00.html#V4" title="GLPACY00:attr.4">Cycle-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83_2_1"><span class="lab"><font color="Green" title="E45">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E3:83_2_1_1"/>
<font color="Maroon" title="c2">G</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:83_2_1"/>
<font color="Maroon" title="c1">S</font> is  <a href="glib_014.html#V9" title="GLIB_014:attr.9">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_014.html#D9" onmouseover="rs('glib_014/D9')" onmouseout="rh()">GLIB_014:def 9</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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