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<b>thus </b><a NAME="E1:21_1_1"/>
not  <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a>  is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>

<a NAME="E2:21_1_1"/><i><font color="Green" title="E17">A1</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#K5" title="SCMFSA_2:func.5">insloc</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>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<b>thus </b><a NAME="E3:21_1_1"/>
 <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a>  is <a href="scmfsa_4.html#V1" title="SCMFSA_4:attr.1">initial</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">m</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="scmfsa_4.html#D4" target="_self" title="SCMFSA_4:def.4">SCMFSA_4:def 4</a><br/><b>let </b><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:21_1_1_1"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c2">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> 
 <b>and </b><br/><a NAME="E2:21_1_1_1"/><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">n</font>
 ;<br/>

<a NAME="E3:21_1_1_1"/>
 <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <font color="Maroon" title="c2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmfsa_2.html#K5" title="SCMFSA_2:func.5">insloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="scmfsa_4.html#E1:21_1_1_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:21_1_1_1"/>
<font color="Maroon" title="c1">m</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a> 
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_1_1_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="nat_1.html#T2" title="NAT_1:th.2">NAT_1:2</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E4:21_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <a href="scmfsa_4.html#K2" title="SCMFSA_4:func.2">SCM+FSA-Stop</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="txt" href="scmfsa_4.html#E2:21_1_1"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="zfmisc_1.html#T37" title="ZFMISC_1:th.37">ZFMISC_1:37</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_1.html#D40" title="AMI_1:def.40">AMI_1:def 40</a><br/>


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