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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E15">Th21</font></span>: <a NAME="T21"><span class="comment"><font color="firebrick">:: GLIB_015:21</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">G</font> being   <a href="glib_000.html#NM2" title="GLIB_000:NM.2">_Graph</a><br/>  for <font color="Olive" title="b2">V</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="glib_000.html#K6" title="GLIB_000:func.6">the_Vertices_of</a> <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b3">E</font> being   <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of  <a href="glib_000.html#K7" title="GLIB_000:func.7">the_Edges_of</a> <font color="Olive" title="b1">G</font><br/>  for <font color="Olive" title="b4">W2</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of  <a href="glib_015.html#K1" title="GLIB_015:func.1">replaceVerticesEdges</a> (<font color="Olive" title="b2">V</font>,<font color="Olive" title="b3">E</font>)  ex <font color="Olive" title="b5">W1</font> being    <a href="glib_001.html#M3" title="GLIB_001:mode.3">Walk</a> of <font color="Olive" title="b1">G</font> st <br/>( <font color="Olive" title="b2">V</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">W1</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">W2</font> <a href="glib_001.html#K11" title="GLIB_001:func.11">.vertexSeq()</a>  &amp; <font color="Olive" title="b3">E</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b5">W1</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">W2</font> <a href="glib_001.html#K12" title="GLIB_001:func.12">.edgeSeq()</a>  )</div></div>
