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<span class="kw">consider </span><font color="Maroon" title="c2">sil</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="scmfsa_2.html#K2" title="SCMFSA_2:func.2">Int-Locations</a><span class="kw"> such that </span><br/><a NAME="E2:63_1_1"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
<font color="Maroon" title="c2">sil</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c1">p</font></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">and </span><br/><a NAME="E3:63_1_1"/><span class="lab"><font color="Green" title="E48">A2</font></span>: 
 <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="sf_mastr.html#K5" title="SF_MASTR:func.5">FirstNotIn</a> <font color="Maroon" title="c2">sil</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#D7" target="_self" title="SF_MASTR:def.7">Def7</a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:63_1_1_1"/>
 <a href="sf_mastr.html#K5" title="SF_MASTR:func.5">FirstNotIn</a> <font color="Maroon" title="c2">sil</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:63_1_1_1"/><span class="kw">then </span>
 not  <a href="scmfsa_2.html#K4" title="SCMFSA_2:func.4">intloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">sil</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="sf_mastr.html#T48" target="_self" title="SF_MASTR:th.48">Th52</a></span>;<br/><span class="kw">hence </span><a NAME="E3:63_1_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:63_1_1"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="setwiseo.html#T4" title="SETWISEO:th.4">SETWISEO:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:63_1_1"/>
 not  <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Maroon" title="c1">p</font> is  <a href="sf_mastr.html#V1" title="SF_MASTR:attr.1">read-only</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63_1_1"><span class="lab"><font color="Green" title="E48">A2</font></span></a>, <a class="ref" href="sf_mastr.html#D5" target="_self" title="SF_MASTR:def.5">Def5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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