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<b>set </b><font color="Maroon" title="c50">IS</font> =  <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> ;<br/>
<b>set </b><font color="Maroon" title="c51">Ii</font> =  <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> ;<br/>
<b>let </b><font color="Maroon" title="c52">i</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"> 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> <br/> for <font color="Olive" title="b2">w</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Olive" title="b2">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">s</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="Olive" title="b1">s</font>,<font color="Maroon" title="c52">i</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> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> </span><br/><b>let </b><font color="Maroon" title="c53">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> ; <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">w</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Olive" title="b1">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c53">s</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="c53">s</font>,<font color="Maroon" title="c52">i</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> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> </span><br/><b>let </b><font color="Maroon" title="c54">w</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c54">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c53">s</font> implies  <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="c53">s</font>,<font color="Maroon" title="c52">i</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> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a>  )</span><br/>





<b>set </b><font color="Maroon" title="c55">x</font> = <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c54">w</font>;<br/>
<b>assume </b><a NAME="E1:64"/><i><font color="Green" title="E52">A1</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c54">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c53">s</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <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="c53">s</font>,<font color="Maroon" title="c52">i</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> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> </span><br/>

<a NAME="E2:64"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c54">w</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T46" title="SCMBSORT:th.46">SCMBSORT:46</a></i>;<br/>
<a NAME="E3:64"/><b>then </b>
 <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K18" title="AMI_1:func.18">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c54">w</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T33" title="FUNCT_4:th.33">FUNCT_4:33</a></i>;<br/>
<a NAME="E4:64"/><b>then </b><i><font color="Green" title="E53">A2</font></i>: 
 <a href="scmfsa6a.html#K4" title="SCMFSA6A:func.4">Initialized</a> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c53">s</font>
 
<b>by </b><i><a class="txt" href="scmisort.html#E1:64"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:64"/>
 <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a>  is  <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> 
 
<b>by </b><i><a class="ref" href="scmisort.html#T44" target="_self" title="SCMISORT:th.44">Th44</a></i>;<br/>
<b>hence </b><a NAME="E6:64"/>
 <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="c53">s</font>,<font color="Maroon" title="c52">i</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> <a href="scmisort.html#K3" title="SCMISORT:func.3">Insert-Sort-Algorithm</a> 
 <b>by </b><i><a class="txt" href="scmisort.html#E4:64"><i><font color="Green" title="E53">A2</font></i></a>, <a class="ref" href="scm_halt.html#D1" title="SCM_HALT:def.1">SCM_HALT:def 1</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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