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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being  <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> <b> such that </b><br/><a NAME="E2:68_1_1"/><i><font color="Green">E49</font></i>: 
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" target="_self">UsedIntLoc</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span><a href="tarski.html#K1">}</a></span> &amp;  <a href="sf_mastr.html#K6" target="_self">FirstNotUsed</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="sf_mastr.html#K5" target="_self">FirstNotIn</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#D7" target="_self">Def7</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="68_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:68_1_1_1"/>
 <a href="sf_mastr.html#K5" target="_self">FirstNotIn</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K4">intloc</a> 0
 ;<br/><a NAME="E2:68_1_1_1"/><b>then </b>
not  <a href="scmfsa_2.html#K4">intloc</a> 0 <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="sf_mastr.html#T52" target="_self">Th52</a></i>;<br/><b>hence </b><a NAME="E3:68_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:68_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="setwiseo.html#T6">SETWISEO:6</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:68_1_1"/>
not  <a href="sf_mastr.html#K6" target="_self">FirstNotUsed</a> <font color="Maroon">c<sub>1</sub></font> is <a href="sf_mastr.html#V1" target="_self">read-only</a>
 <b>by </b><i><a class="txt" href="sf_mastr.html#E2:68_1_1"><i><font color="Green">E49</font></i></a>, <a class="ref" href="sf_mastr.html#D5" target="_self">Def5</a></i>;<br/>


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