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<span class="kw">let </span><font color="Maroon" title="c1">G1</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">G2</font> being    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b2">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b3">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">G2</font>  st <font color="Olive" title="b2">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">v2</font> holds <br/>( <font color="Olive" title="b3">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b2">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <font color="Olive" title="b3">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b2">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  &amp; <font color="Olive" title="b3">v2</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> <font color="Olive" title="b2">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">G2</font> be    <a href="glib_000.html#M1" title="GLIB_000:mode.1">Subgraph</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">  for <font color="Olive" title="b1">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c1">G1</font><br/>  for <font color="Olive" title="b2">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Olive" title="b1">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">v2</font> holds <br/>( <font color="Olive" title="b2">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <font color="Olive" title="b2">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Olive" title="b1">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  &amp; <font color="Olive" title="b2">v2</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> <font color="Olive" title="b1">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">v1</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">  for <font color="Olive" title="b1">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Maroon" title="c2">G2</font>  st <font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v2</font> holds <br/>( <font color="Olive" title="b1">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <font color="Olive" title="b1">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  &amp; <font color="Olive" title="b1">v2</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> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">v2</font> be   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <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">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">v2</font> implies ( <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  &amp; <font color="Maroon" title="c4">v2</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> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  ) )</span><br/>







<span class="kw">assume </span><a NAME="E1:2"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<font color="Maroon" title="c3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <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="c4">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  &amp; <font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  &amp; <font color="Maroon" title="c4">v2</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> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  )</span><br/>

<a NAME="E2:2"/><span class="kw">then </span>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K26" title="GLIB_000:func.26">.edgesIn()</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#T78" onmouseover="rs('glib_000/T78')" onmouseout="rh()">GLIB_000:78</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:2"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K30" title="GLIB_000:func.30">.inDegree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="card_1.html#T11" onmouseover="rs('card_1/T11')" onmouseout="rh()">CARD_1:11</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="c4">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  &amp; <font color="Maroon" title="c4">v2</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> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:2"/>
<font color="Maroon" title="c4">v2</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a>  <a href="ordinal1.html#R1" title="ORDINAL1:pred.1">c=</a> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K31" title="GLIB_000:func.31">.outDegree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:2"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="ref" href="glib_000.html#T78" onmouseover="rs('glib_000/T78')" onmouseout="rh()">GLIB_000:78</a>, <a class="ref" href="card_1.html#T11" onmouseover="rs('card_1/T11')" onmouseout="rh()">CARD_1:11</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="c4">v2</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> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a> </span><br/>

<span class="kw">hence </span><a NAME="E5:2"/>
<font color="Maroon" title="c4">v2</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> <font color="Maroon" title="c3">v1</font> <a href="glib_000.html#K34" title="GLIB_000:func.34">.degree()</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:2"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="card_2.html#T83" onmouseover="rs('card_2/T83')" onmouseout="rh()">CARD_2:83</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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