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<b>let </b><font color="Maroon" title="c1">G1</font>, <font color="Maroon" title="c2">G2</font> be   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c1">G1</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> implies <font color="Maroon" title="c2">G2</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> )</span><br/>



<b>assume </b><a NAME="E1:80"/><i><font color="Green" title="E48">A1</font></i>: 
( <font color="Maroon" title="c1">G1</font> <a href="glib_000.html#R5" title="GLIB_000:pred.5">==</a> <font color="Maroon" title="c2">G2</font> &amp; <font color="Maroon" title="c1">G1</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">G2</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a></span><br/>

<a NAME="E2:80"/><b>then </b>
( <font color="Maroon" title="c1">G1</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> &amp; <font color="Maroon" title="c1">G1</font> is <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a> )
 
<b>by </b><i><a class="ref" href="glib_002.html#D3" target="_self" title="GLIB_002:def.3">Def3</a></i>;<br/>
<a NAME="E3:80"/><b>then </b>
( <font color="Maroon" title="c2">G2</font> is <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> &amp; <font color="Maroon" title="c2">G2</font> is <a href="glib_002.html#V2" title="GLIB_002:attr.2">acyclic</a> )
 
<b>by </b><i><a class="txt" href="glib_002.html#E1:80"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="glib_002.html#T8" target="_self" title="GLIB_002:th.8">Th8</a>, <a class="ref" href="glib_002.html#T44" target="_self" title="GLIB_002:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E4:80"/>
<font color="Maroon" title="c2">G2</font> is <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>
 <b>by </b><i><a class="ref" href="glib_002.html#D3" target="_self" title="GLIB_002:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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