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<b>let </b><font color="Maroon">a</font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>let </b><font color="Maroon">k</font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:54_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">k</font></span>)</span>
 ;<br/><a NAME="E2:54_1"/>
<font color="Maroon">a</font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_7.html#K1">Load</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#T33">SCMFSA_7:33</a></i>;<br/><b>then </b> <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">k</font></span>)</span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span></span>)</span> <a href="xboole_0.html#K2">\/</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2"><a href="binarith.html#K11">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="binarith.html#K11">*&gt;</a></span></span>)</span>
<b>by </b><i><a class="ref" href="finseq_1.html#T44">FINSEQ_1:44</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <span class="p2">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span></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="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1">}</a></span>
<b>by </b><i><a class="ref" href="finseq_1.html#T55">FINSEQ_1:55</a></i>
;<br/><a NAME="E4:54_1"/><b>then </b><i><font color="Green">E28</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><a NAME="E5:54_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="scmfsa_7.html#K3">aSeq</a> <font color="Maroon">a</font>,<font color="Maroon">k</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span><a href="enumset1.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="scmfsa7b.html#E4:54_1"><i><font color="Green">E28</font></i></a></i>;<br/><a NAME="E6:54_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a>  <a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a>  )
 <b>by </b><i>, <a class="ref" href="enumset1.html#D1">ENUMSET1:def 1</a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E7:54_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="enumset1.html#D2">ENUMSET1:def 2</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:54"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_7.html#K2">:=</a> <font color="Maroon">k</font></span>)</span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="enumset1.html#K2">{</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">a</font> <a href="scmfsa_2.html#K8">:=</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span><a href="enumset1.html#K2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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