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<div>:: <span class="kw">deftheorem </span>   defines <a href="sgraph1.html#K6" title="SGRAPH1:func.6">K_</a> <a onclick="hs(this)" href="javascript:()">SGRAPH1:def 12 : <br/></a><span> for <font color="Olive" title="b1">n</font>, <font color="Olive" title="b2">m</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive">b<sub>3</sub></font> being    <a href="sgraph1.html#M1" title="SGRAPH1:mode.1">SimpleGraph</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  holds <br/> ( <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sgraph1.html#K6" title="SGRAPH1:func.6">K_</a> (<font color="Olive" title="b2">m</font>,<font color="Olive" title="b1">n</font>) iff  ex <font color="Olive" title="b4">ee</font> being   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="sgraph1.html#K2" title="SGRAPH1:func.2">TWOELEMENTSETS</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span></span>)</span> st <br/>( <font color="Olive" title="b4">ee</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b5">i</font>,<font color="Olive" title="b6">j</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> where <font color="Olive" title="b5">i</font>, <font color="Olive" title="b6">j</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  : ( <font color="Olive" title="b5">i</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Olive" title="b2">m</font> &amp; <font color="Olive" title="b6">j</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="sgraph1.html#K1" title="SGRAPH1:func.1">nat_interval</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b1">n</font></span>)</span>) ) </span> } </span>  &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sgraph1.html#G1" title="SGRAPH1:aggr.1">SimpleGraphStruct</a>(# <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> <font color="Olive" title="b1">n</font></span>)</span></span>)</span>,<font color="Olive" title="b4">ee</font> #) ) );<br/></span></div>
