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<span class="kw">let </span><font color="Maroon" title="c1">P</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="c1">P</font> is  <a href="glpacy00.html#V1" title="GLPACY00:attr.1">Path-like</a>  implies ( <font color="Maroon" title="c1">P</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>  &amp; <font color="Maroon" title="c1">P</font> is  <a href="glib_013.html#V5" title="GLIB_013:attr.5">locally-finite</a>  &amp; <font color="Maroon" title="c1">P</font> is  <a href="glib_013.html#V6" title="GLIB_013:attr.6">with_max_degree</a>  ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:14_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c1">P</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">P</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-like</a>  &amp; <font color="Maroon" title="c1">P</font> is  <a href="glib_013.html#V5" title="GLIB_013:attr.5">locally-finite</a>  &amp; <font color="Maroon" title="c1">P</font> is  <a href="glib_013.html#V6" title="GLIB_013:attr.6">with_max_degree</a>  )</span><br/>

<span class="kw">hence </span><a NAME="E2:14_1_1"/>
<font color="Maroon" title="c1">P</font> is  <a href="glib_002.html#V3" title="GLIB_002:attr.3">Tree-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">P</font> is  <a href="glib_013.html#V5" title="GLIB_013:attr.5">locally-finite</a>  &amp; <font color="Maroon" title="c1">P</font> is  <a href="glib_013.html#V6" title="GLIB_013:attr.6">with_max_degree</a>  )</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="14_1_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">v</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">P</font> holds  <font color="Olive" title="b1">v</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span></a><div class="add"><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">P</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> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> </span><br/><a NAME="E1:14_1_1_1"/>
<font color="Maroon" title="c2">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="#E1:14_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E2:14_1_1_1"/>
<font color="Maroon" title="c2">v</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  is  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</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="E4:14_1_1"/>
<font color="Maroon" title="c1">P</font> is  <a href="glib_013.html#V5" title="GLIB_013:attr.5">locally-finite</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="glib_013.html#T23" onmouseover="rs('glib_013/T23')" onmouseout="rh()">GLIB_013:23</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"> <font color="Maroon" title="c1">P</font> is  <a href="glib_013.html#V6" title="GLIB_013:attr.6">with_max_degree</a> </span><br/>

<span class="kw">thus </span><a NAME="E5:14_1_1"/>
<font color="Maroon" title="c1">P</font> is  <a href="glib_013.html#V6" title="GLIB_013:attr.6">with_max_degree</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:14_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="glpacy00.html#E12"><span class="lab"><font color="Green" title="E12">Th13</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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