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<b>let </b><font color="Maroon" title="c1">N</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="setfam_1.html#V1" title="SETFAM_1:attr.1">with_non-empty_elements</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">S</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V6" title="AMI_1:attr.6">steady-programmed</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font><br/> for <font color="Olive" title="b2">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b3">f</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Olive" title="b1">S</font><br/> for <font color="Olive" title="b4">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">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="Olive" title="b3">f</font> &amp; <font color="Olive" title="b3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Olive" title="b1">S</font> holds <br/> <a href="scmnorm.html#K12" title="SCMNORM:func.12">Result</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b2">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">k</font></span><br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="ami_1.html#V4" title="AMI_1:attr.4">halting</a> <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> <a href="ami_1.html#V6" title="AMI_1:attr.6">steady-programmed</a>  <a href="ami_1.html#L1" title="AMI_1:struct.1">AMI-Struct</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,<font color="Maroon" title="c1">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">s</font> being  <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <font color="Maroon" title="c2">S</font><br/> for <font color="Olive" title="b2">f</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c2">S</font><br/> for <font color="Olive" title="b3">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">s</font>,<font color="Olive" title="b3">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="Olive" title="b2">f</font> &amp; <font color="Olive" title="b2">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">s</font>,<font color="Olive" title="b3">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> holds <br/> <a href="scmnorm.html#K12" title="SCMNORM:func.12">Result</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b1">s</font>,<font color="Olive" title="b3">k</font></span><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 <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c2">S</font><br/> for <font color="Olive" title="b2">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b2">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="Olive" title="b1">f</font> &amp; <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b2">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> holds <br/> <a href="scmnorm.html#K12" title="SCMNORM:func.12">Result</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Olive" title="b1">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b2">k</font></span><br/><b>let </b><font color="Maroon" title="c4">f</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ,the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <font color="Maroon" title="c2">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<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="c4">f</font> &amp; <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b1">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> holds <br/> <a href="scmnorm.html#K12" title="SCMNORM:func.12">Result</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Olive" title="b1">k</font></span><br/><b>let </b><font color="Maroon" title="c5">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">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="c4">f</font> &amp; <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> implies  <a href="scmnorm.html#K12" title="SCMNORM:func.12">Result</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font> )</span><br/>









<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E10">A0</font></i>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">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="c4">f</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font> or  <a href="scmnorm.html#K12" title="SCMNORM:func.12">Result</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font> )</span><br/>

<b>assume </b><a NAME="E2:37"/>
<font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p2">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="scmnorm.html#K12" title="SCMNORM:func.12">Result</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font></span><br/>

<a NAME="E3:37"/><b>then </b><i><font color="Green" title="E11">A2</font></i>: 
 <a href="scmnorm.html#K9" title="SCMNORM:func.9">CurInstr</a> <font color="Maroon" title="c4">f</font>,<span class="p1">(<span class="default"><a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="txt" href="#E1:37"><i><font color="Green" title="E10">A0</font></i></a>, <a class="ref" href="scmnorm.html#D4" target="_self" title="SCMNORM:def.4">Def4</a></i>;<br/>
<a NAME="E4:37"/><b>then </b>
<font color="Maroon" title="c4">f</font> <a href="scmnorm.html#R1" title="SCMNORM:pred.1">halts_on</a> <font color="Maroon" title="c3">s</font>
 
<b>by </b><i><a class="txt" href="#E1:37"><i><font color="Green" title="E10">A0</font></i></a>, <a class="ref" href="scmnorm.html#D8" target="_self" title="SCMNORM:def.8">Def8</a></i>;<br/>
<b>hence </b><a NAME="E5:37"/>
 <a href="scmnorm.html#K12" title="SCMNORM:func.12">Result</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K11" title="SCMNORM:func.11">Comput</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c3">s</font>,<font color="Maroon" title="c5">k</font>
 <b>by </b><i><a class="txt" href="#E3:37"><i><font color="Green" title="E11">A2</font></i></a>, <a class="ref" href="scmnorm.html#D10" target="_self" title="SCMNORM:def.10">Def10</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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