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<div><span class="kw">theorem </span><a NAME="T111"><span class="comment"><font color="firebrick">:: GLIBPRE1:111</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G1</font> being   <a href="glib_000.html#V8" title="GLIB_000:attr.8">Dsimple</a>   <a href="glib_013.html#V1" title="GLIB_013:attr.1">vertex-finite</a>  <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><br/>  for <font color="Olive" title="b2">G2</font> being    <a href="glib_012.html#M4" title="GLIB_012:mode.4">DGraphComplement</a> of <font color="Olive" title="b1">G1</font><br/>  for <font color="Olive" title="b3">v1</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b1">G1</font><br/>  for <font color="Olive" title="b4">v2</font> being   <a href="glib_000.html#NM10" title="GLIB_000:NM.10">Vertex</a> of <font color="Olive" title="b2">G2</font>  st <font color="Olive" title="b3">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">v2</font> holds <br/>( <font color="Olive" title="b4">v2</font> <a href="glib_013.html#K3" title="GLIB_013:func.3">.inDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">G1</font> <a href="glib_013.html#K1" title="GLIB_013:func.1">.order()</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">v1</font> <a href="glib_013.html#K3" title="GLIB_013:func.3">.inDegree()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Olive" title="b4">v2</font> <a href="glib_013.html#K4" title="GLIB_013:func.4">.outDegree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">G1</font> <a href="glib_013.html#K1" title="GLIB_013:func.1">.order()</a></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">v1</font> <a href="glib_013.html#K4" title="GLIB_013:func.4">.outDegree()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Olive" title="b4">v2</font> <a href="glib_013.html#K5" title="GLIB_013:func.5">.degree()</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">2 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">G1</font> <a href="glib_013.html#K1" title="GLIB_013:func.1">.order()</a></span>)</span></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b3">v1</font> <a href="glib_013.html#K5" title="GLIB_013:func.5">.degree()</a></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span> )</div></div>
