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<b>let </b><font color="Maroon" title="c2">s1</font>, <font color="Maroon" title="c3">s2</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> ; <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">I</font> being <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a>   st  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s1</font> &amp;  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s2</font> &amp; <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds <br/>for <font color="Olive" title="b2">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 <br/> (  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b2">k</font>, <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Olive" title="b2">k</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b2">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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">s2</font>,<font color="Olive" title="b2">k</font></span>)</span> )</span><br/><b>let </b><font color="Maroon" title="c4">I</font> be  <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a> <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmfsa_2.html#K1" title="SCMFSA_2:func.1">SCM+FSA</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s1</font> &amp;  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s2</font> &amp; <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  implies 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 <br/> (  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">k</font>, <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Olive" title="b1">k</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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">s2</font>,<font color="Olive" title="b1">k</font></span>)</span> ) )</span><br/>





<b>assume </b><b>that </b><br/><a NAME="E1:20"/><i><font color="Green" title="E15">A1</font></i>: 
 <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s1</font>
 <b>and </b><br/><a NAME="E2:20"/><i><font color="Green" title="E16">A2</font></i>: 
 <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s2</font>
 <b>and </b><br/><a NAME="E3:20"/><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c3">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <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"> 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 <br/> (  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">k</font>, <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Olive" title="b1">k</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Olive" title="b1">k</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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">s2</font>,<font color="Olive" title="b1">k</font></span>)</span> )</span><br/>

<a NAME="E4:20"/><i><font color="Green" title="E18">A4</font></i>: 
<font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">s1</font>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E1:20"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="scm_halt.html#T13" target="_self" title="SCM_HALT:th.13">Th13</a></i>;<br/>
<a NAME="E5:20"/><i><font color="Green" title="E19">A5</font></i>: 
<font color="Maroon" title="c4">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s2</font>
 
<b>by </b><i><a class="txt" href="scm_halt.html#E2:20"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scm_halt.html#T13" target="_self" title="SCM_HALT:th.13">Th13</a></i>;<br/>
<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span>
<div class="add"><b>let </b><font color="Maroon" title="c5">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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c5">k</font>, <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c5">k</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  &amp;  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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">s2</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#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c5">k</font></span>)</span> )</span><br/><a NAME="E1:20_1"/>
for <font color="Olive" title="b1">m</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>   st <font color="Olive" title="b1">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c5">k</font> holds <br/> <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">s2</font>,<font color="Olive" title="b1">m</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">I</font>
 <b>by </b><i><a class="txt" href="scm_halt.html#E2:20"><i><font color="Green" title="E16">A2</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="E2:20_1"/>
 <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c5">k</font>, <a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c5">k</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <b>by </b><i><a class="txt" href="scm_halt.html#E3:20"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="scm_halt.html#E4:20"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="scm_halt.html#E5:20"><i><font color="Green" title="E19">A5</font></i></a>, <a class="ref" href="scmfsa6b.html#T21" title="SCMFSA6B:th.21">SCMFSA6B:21</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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">s2</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#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c5">k</font></span>)</span></span><br/><a NAME="E3:20_1"/><b>then </b><i><font color="Green" title="E20">A6</font></i>: 
 <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="c2">s1</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#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">s2</font>,<font color="Maroon" title="c5">k</font></span>)</span>
 <b>by </b><i><a class="ref" href="ami_1.html#T121" title="AMI_1:th.121">AMI_1:121</a></i>;<br/><a NAME="E4:20_1"/><i><font color="Green" title="E21">A7</font></i>: 
 <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="c2">s1</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">I</font>
 <b>by </b><i><a class="txt" href="scm_halt.html#E1:20"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="scm_halt.html#D1" target="_self" title="SCM_HALT:def.1">Def1</a></i>;<br/><a NAME="E5:20_1"/><i><font color="Green" title="E22">A8</font></i>: 
 <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">s2</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">I</font>
 <b>by </b><i><a class="txt" href="scm_halt.html#E2:20"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="scm_halt.html#D1" target="_self" title="SCM_HALT:def.1">Def1</a></i>;<br/><b>thus </b> <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</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">s2</font>,<font color="Maroon" title="c5">k</font></span>)</span> = 
<font color="Maroon" title="c3">s2</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
<br/>.= 
<font color="Maroon" title="c4">I</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c3">s2</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scm_halt.html#E5:20"><i><font color="Green" title="E19">A5</font></i></a>, <a class="txt" href="scm_halt.html#E5:20_1"><i><font color="Green" title="E22">A8</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
<font color="Maroon" title="c2">s1</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c5">k</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scm_halt.html#E4:20"><i><font color="Green" title="E18">A4</font></i></a>, <a class="txt" href="scm_halt.html#E3:20_1"><i><font color="Green" title="E20">A6</font></i></a>, <a class="txt" href="scm_halt.html#E4:20_1"><i><font color="Green" title="E21">A7</font></i></a>, <a class="ref" href="grfunc_1.html#T8" title="GRFUNC_1:th.8">GRFUNC_1:8</a></i>
<br/>.= 
 <a href="ami_1.html#K8" title="AMI_1:func.8">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Computation</a> <font color="Maroon" title="c2">s1</font>,<font color="Maroon" title="c5">k</font></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#T54" title="AMI_1:th.54">AMI_1:54</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>


</div>
