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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: GLIB_000:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">GS</font> being   <a href="glib_000.html#NM1" title="GLIB_000:NM.1">GraphStruct</a><br/>  for <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b4">n1</font>, <font color="Olive" title="b5">n2</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <font color="Olive" title="b4">n1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b5">n2</font> holds <br/>( <font color="Olive" title="b4">n1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">GS</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> (<font color="Olive" title="b4">n1</font>,<font color="Olive" title="b2">x</font>)</span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> (<font color="Olive" title="b5">n2</font>,<font color="Olive" title="b3">y</font>)</span>)</span> &amp; <font color="Olive" title="b5">n2</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">GS</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> (<font color="Olive" title="b4">n1</font>,<font color="Olive" title="b2">x</font>)</span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> (<font color="Olive" title="b5">n2</font>,<font color="Olive" title="b3">y</font>)</span>)</span> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">GS</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> (<font color="Olive" title="b4">n1</font>,<font color="Olive" title="b2">x</font>)</span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> (<font color="Olive" title="b5">n2</font>,<font color="Olive" title="b3">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b4">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Olive" title="b1">GS</font> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> (<font color="Olive" title="b4">n1</font>,<font color="Olive" title="b2">x</font>)</span>)</span> <a href="glib_000.html#K13" title="GLIB_000:func.13">.set</a> (<font color="Olive" title="b5">n2</font>,<font color="Olive" title="b3">y</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b5">n2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">y</font> )</div></div>
