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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">E</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">G1</font> being    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G2</font>,<font color="Olive" title="b1">E</font> holds <br/> ( <font color="Olive" title="b2">G1</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G2</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a>  &amp; <font color="Olive" title="b2">G1</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G2</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">E</font> be    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">E</font> holds <br/> ( <font color="Olive" title="b1">G1</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G2</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a>  &amp; <font color="Olive" title="b1">G1</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G2</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">G1</font> be    <a href="glib_007.html#M1" title="GLIB_007:mode.1">reverseEdgeDirections</a> of <font color="Maroon" title="c1">G2</font>,<font color="Maroon" title="c2">E</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">G1</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G2</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a>  &amp; <font color="Maroon" title="c3">G1</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G2</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a>  )</span><br/>





<a NAME="E1:32"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
(  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c3">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c1">G2</font> &amp;  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c3">G1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c1">G2</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_007.html#T4" target="_self" onmouseover="rs('glib_007/T4')" onmouseout="rh()">Th4</a></span>;<br/>
<span class="kw">thus </span><font color="Maroon" title="c3">G1</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a>  = 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Maroon" title="c3">G1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D24" onmouseover="rs('glib_000/D24')" onmouseout="rh()">GLIB_000:def 24</a></span>
<br/>.= 
<font color="Maroon" title="c1">G2</font> <a href="glib_000.html#K14" title="GLIB_000:func.14">.order()</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="glib_000.html#D24" onmouseover="rs('glib_000/D24')" onmouseout="rh()">GLIB_000:def 24</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="c3">G1</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">G2</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a> </span><br/>

<span class="kw">thus </span><font color="Maroon" title="c3">G1</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a>  = 
 <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <span class="p1">(<span class="default"><a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Maroon" title="c3">G1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="glib_000.html#D25" onmouseover="rs('glib_000/D25')" onmouseout="rh()">GLIB_000:def 25</a></span>
<br/>.= 
<font color="Maroon" title="c1">G2</font> <a href="glib_000.html#K16" title="GLIB_000:func.16">.size()</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="glib_000.html#D25" onmouseover="rs('glib_000/D25')" onmouseout="rh()">GLIB_000:def 25</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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