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<span class="kw">let </span><font color="Maroon" title="c1">P1</font> be   <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  <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">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">P1</font><br/>  for <font color="Olive" title="b2">P2</font> being   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c1">P1</font>,<font color="Olive" title="b1">v</font>  st ( <font color="Olive" title="b1">v</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  or <font color="Maroon" title="c1">P1</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>  ) holds <br/><font color="Olive" title="b2">P2</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">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">P1</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">  for <font color="Olive" title="b1">P2</font> being   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c1">P1</font>,<font color="Maroon" title="c2">v</font>  st ( <font color="Maroon" title="c2">v</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  or <font color="Maroon" title="c1">P1</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>  ) holds <br/><font color="Olive" title="b1">P2</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="c3">P2</font> be   <a href="glib_000.html#NM6" title="GLIB_000:NM.6">removeVertex</a> of <font color="Maroon" title="c1">P1</font>,<font color="Maroon" title="c2">v</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">v</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  or <font color="Maroon" title="c1">P1</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>  ) implies <font color="Maroon" title="c3">P2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:43"/>
( <font color="Maroon" title="c2">v</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  or <font color="Maroon" title="c1">P1</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</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="c3">P2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a> </span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:43_1"/><span class="kw">then </span>
( (  not <font color="Maroon" title="c1">P1</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>  &amp; <font color="Maroon" title="c2">v</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</a>  ) or <font color="Maroon" title="c1">P1</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_1"><span class="kw">suppose </span></a><a NAME="E1:43_1_1"/>
(  not <font color="Maroon" title="c1">P1</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</a>  &amp; <font color="Maroon" title="c2">v</font> is  <a href="glib_000.html#V11" title="GLIB_000:attr.11">endvertex</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="c3">P2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a> </span><br/><div class="add"><a NAME="E2:43_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c3">P2</font> is  <a href="glib_002.html#V1" title="GLIB_002:attr.1">connected</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_002.html#T4" onmouseover="rs('glib_002/T4')" onmouseout="rh()">GLIB_002:4</a></span>;<br/><span class="kw">hence </span><a NAME="E3:43_1_1"/>
<font color="Maroon" title="c3">P2</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"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="43_1_2"><span class="kw">suppose </span></a><a NAME="E1:43_1_2"/>
<font color="Maroon" title="c1">P1</font> is  <a href="glib_000.html#V4" title="GLIB_000:attr.4">_trivial</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="c3">P2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a> </span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:43_1_2"/>
<font color="Maroon" title="c3">P2</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"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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