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<b>let </b><font color="Maroon" title="c2">I</font> be   <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:53_1"/><i><font color="Green" title="E38">A1</font></i>: 
<font color="Maroon" title="c2">I</font> is <a href="scm_halt.html#V1" title="SCM_HALT:attr.1">InitClosed</a>
 ;<br/><b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><a NAME="E2:53_1"/>
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c2">I</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_4.html#T26" title="FUNCT_4:th.26">FUNCT_4:26</a></i>;<br/><a NAME="E3:53_1"/><b>then </b>
for <font color="Olive" title="b1">k</font> being   <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>  holds   <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p3">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c2">I</font></span>)</span></span>)</span>,<font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">I</font>
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:53_1"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="scm_halt.html#D1" target="_self" title="SCM_HALT:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E4:53_1"/>
<font color="Maroon" title="c2">I</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c3">s</font>
 <b>by </b><i><a class="ref" href="scm_halt.html#D4" target="_self" title="SCM_HALT:def.4">Def4</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:53"/><i><font color="Green" title="E38">A2</font></i>: 
for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>  holds  <font color="Maroon" title="c2">I</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Olive" title="b1">s</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="53_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ;<br/><b>let </b><font color="Maroon" title="c4">k</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><a NAME="E1:53_2"/>
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s</font>
 ;<br/><a NAME="E2:53_2"/><b>then </b>
( <font color="Maroon" title="c2">I</font> <a href="scm_halt.html#R1" title="SCM_HALT:pred.1">is_closed_onInit</a> <font color="Maroon" title="c3">s</font> &amp; <font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s</font> <a href="ami_1.html#K34" title="AMI_1:func.34">+*</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <font color="Maroon" title="c2">I</font></span>)</span> )
 <b>by </b><i><a class="txt" href="scm_halt.html#E2:53"><i><font color="Green" title="E38">A2</font></i></a>, <a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></i>;<br/><b>hence </b><a NAME="E3:53_2"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c4">k</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">I</font>
 <b>by </b><i><a class="ref" href="scm_halt.html#D4" target="_self" title="SCM_HALT:def.4">Def4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:53"/>
<font color="Maroon" title="c2">I</font> is <a href="scm_halt.html#V1" title="SCM_HALT:attr.1">InitClosed</a>
 <b>by </b><i><a class="ref" href="scm_halt.html#D1" target="_self" title="SCM_HALT:def.1">Def1</a></i>;<br/>


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