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<span class="kw">let </span><font color="Maroon" title="c1">G2</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">  for <font color="Olive" title="b1">v1</font>, <font color="Olive" title="b2">e</font>, <font color="Olive" title="b3">v2</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <br/>  for <font color="Olive" title="b4">G1</font> being    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Olive" title="b1">v1</font>,<font color="Olive" title="b2">e</font>,<font color="Olive" title="b3">v2</font>  st <font color="Olive" title="b4">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  holds <br/><font color="Maroon" title="c1">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">v1</font>, <font color="Maroon" title="c3">e</font>, <font color="Maroon" title="c4">v2</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</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">  for <font color="Olive" title="b1">G1</font> being    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c4">v2</font>  st <font color="Olive" title="b1">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  holds <br/><font color="Maroon" title="c1">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">G1</font> be    <a href="glib_006.html#M4" title="GLIB_006:mode.4">addAdjVertex</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">v1</font>,<font color="Maroon" title="c3">e</font>,<font color="Maroon" title="c4">v2</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="c5">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  implies <font color="Maroon" title="c1">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:42"/><span class="lab"><font color="Green" title="E24">A1</font></span>: 
<font color="Maroon" title="c5">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-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">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a> </span><br/>

<a NAME="E2:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A2</font></span>: 
<font color="Maroon" title="c1">G2</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> 
 
;<br/>
<a NAME="E3:42"/>
<font color="Maroon" title="c1">G2</font> is    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c5">G1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_006.html#T57" onmouseover="rs('glib_006/T57')" onmouseout="rh()">GLIB_006:57</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:42"/>
<font color="Maroon" title="c1">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:42"><span class="lab"><font color="Green" title="E24">A1</font></span></a>, <a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E25">A2</font></span></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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