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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <a href="scmfsa_2.html#K2">Int-Locations</a> ;<br/>

<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="sf_mastr.html#K5" target="_self">FirstNotIn</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E2:65"/><i><font color="Green">E48</font></i>: 
 <a href="sf_mastr.html#K5" target="_self">FirstNotIn</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K4">intloc</a> <span class="p1">(<span class="default"><a href="cqc_sim1.html#K10">min</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E3:65"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="nat_1.html#NM1">Nat</a> : not  <a href="scmfsa_2.html#K4">intloc</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> </span>}</span> 
 <b>by </b><i><a class="ref" href="sf_mastr.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E4:65"/>
 <a href="cqc_sim1.html#K10">min</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="cqc_sim1.html#D8">CQC_SIM1:def 8</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E6:65"/><i><font color="Green">E50</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="cqc_sim1.html#K10">min</a> <font color="Maroon">c<sub>3</sub></font> &amp; not  <a href="scmfsa_2.html#K4">intloc</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="sf_mastr.html#E3:65"><i><font color="Green">E49</font></i></a></i>;<br/>
<b>thus </b><a NAME="E7:65"/>
not  <a href="sf_mastr.html#K5" target="_self">FirstNotIn</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:65"><i><font color="Green">E48</font></i></a>, <a class="txt" href="sf_mastr.html#E6:65"><i><font color="Green">E50</font></i></a></i>;<br/>


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