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<b>let </b><font color="Maroon">I</font> be   <a href="scmfsa6a.html#NM1">Macro-Instruction</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:44_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">I</font> is <a href="scmfsa6b.html#V1">paraclosed</a>
 ;<br/><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><a NAME="E2:44_1"/>
<font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T26">FUNCT_4:26</a></i>;<br/><a NAME="E3:44_1"/><b>then </b>
for <font color="Olive">k</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>  holds   <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <span class="p3">(<span class="default"><font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p4">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p5">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p0">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Olive">k</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T1" target="_self">Th1</a>, <a class="ref" href="scmfsa6b.html#D2">SCMFSA6B:def 2</a></i>;<br/><b>hence </b><a NAME="E4:44_1"/>
<font color="Maroon">I</font> <a href="scmfsa7b.html#R5" target="_self">is_closed_on</a> <font color="Maroon">s</font>
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:44"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">s</font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a>  holds  <font color="Maroon">I</font> <a href="scmfsa7b.html#R5" target="_self">is_closed_on</a> <font color="Olive">s</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">s</font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmfsa_2.html#K1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:44_2"/>
<font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p1">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p2">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">s</font>
 ;<br/><a NAME="E2:44_2"/><b>then </b>
( <font color="Maroon">I</font> <a href="scmfsa7b.html#R5" target="_self">is_closed_on</a> <font color="Maroon">s</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="ami_5.html#K8">+*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="ami_1.html#K17">+*</a> <span class="p2">(<span class="default"><a href="ami_3.html#K12">Start-At</a> <span class="p3">(<span class="default"><a href="scmfsa_2.html#K5">insloc</a> 0</span>)</span></span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="scmfsa7b.html#T1" target="_self">Th1</a>, <a class="ref" href="funct_4.html#T79">FUNCT_4:79</a></i>;<br/><b>hence </b><a NAME="E3:44_2"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">s</font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">I</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:44"/>
<font color="Maroon">I</font> is <a href="scmfsa6b.html#V1">paraclosed</a>
 <b>by </b><i><a class="ref" href="scmfsa6b.html#D2">SCMFSA6B:def 2</a></i>;<br/>


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