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<b>let </b><font color="Maroon" title="c1">p</font> be   <a href="scmnorm.html#NM1" title="SCMNORM:NM.1">preProgram</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not  <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c1">p</font></span><br/>

<b>consider </b><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> <b> such that </b><br/><a NAME="E2:65"/><i><font color="Green" title="E48">A1</font></i>: 
( <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> &amp;  <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> )
 <b>by </b><i><a class="ref" href="sf_mastr.html#D7" target="_self" title="SF_MASTR:def.7">Def7</a></i>;<br/>
<a NAME="E3:65"/>
not  <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">sil</font>
 
<b>by </b><i><a class="txt" href="#E2:65"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="sf_mastr.html#T52" target="_self" title="SF_MASTR:th.52">Th52</a></i>;<br/>
<b>hence </b><a NAME="E4:65"/>
not  <a href="sf_mastr.html#K6" title="SF_MASTR:func.6">FirstNotUsed</a> <font color="Maroon" title="c1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="sf_mastr.html#K2" title="SF_MASTR:func.2">UsedIntLoc</a> <font color="Maroon" title="c1">p</font>
 <b>by </b><i><a class="txt" href="#E2:65"><i><font color="Green" title="E48">A1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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