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<span class="kw">let </span><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" 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">F</font> being    <a href="glib_010.html#M1" title="GLIB_010:mode.1">PGraphMapping</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</font>  st <font color="Olive" title="b1">F</font> is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</a>  &amp; <font color="Maroon" title="c2">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  holds <br/><font color="Maroon" title="c1">G1</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">F</font> be    <a href="glib_010.html#M1" title="GLIB_010:mode.1">PGraphMapping</a> of <font color="Maroon" title="c1">G1</font>,<font color="Maroon" title="c2">G2</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="c3">F</font> is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</a>  &amp; <font color="Maroon" title="c2">G2</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  implies <font color="Maroon" title="c1">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:50"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
( <font color="Maroon" title="c3">F</font> is  <a href="glib_010.html#V17" title="GLIB_010:attr.17">isomorphism</a>  &amp; <font color="Maroon" title="c2">G2</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">G1</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a> </span><br/>

<a NAME="E2:50"/><span class="kw">then </span>
( <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>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_010.html#T140" onmouseover="rs('glib_010/T140')" onmouseout="rh()">GLIB_010:140</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:50"/>
<font color="Maroon" title="c1">G1</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="glpacy00.html#D1" target="_self" onmouseover="rs('glpacy00/D1')" onmouseout="rh()">GLPACY00:def 1</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">G1</font> holds  <font color="Olive" title="b1">v</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> 2</span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">v</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</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="c4">v</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> 2</span><br/>

<a NAME="E4:50"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="glib_010.html#K5" title="GLIB_010:func.5">_V</a></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <font color="Maroon" title="c4">v</font></span>)</span> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E30">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:50"/>
<font color="Maroon" title="c4">v</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> 2
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:50"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="ref" href="glibpre0.html#T93" onmouseover="rs('glibpre0/T93')" onmouseout="rh()">GLIBPRE0:93</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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