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<b>set </b><font color="Maroon" title="c39">Ba</font> =  <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> ;<br/>
<b>set </b><font color="Maroon" title="c40">Ib</font> =  <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> ;<br/>
<b>let </b><font color="Maroon" title="c41">i</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> ;<br/><b>let </b><font color="Maroon" title="c42">s</font> be   <a href="ami_1.html#NM4" title="AMI_1:NM.4">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="c43">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> ;<br/>





<b>set </b><font color="Maroon" title="c44">x</font> = <span class="p1">(<span class="default"><a href="scmfsa_2.html#K6" title="SCMFSA_2:func.6">fsloc</a> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c43">w</font>;<br/>
<b>assume </b><a NAME="E1:67"/><i><font color="Green" title="E65">A1</font></i>: 
<span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</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> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c43">w</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c42">s</font>
 ;<br/>

<a NAME="E2:67"/>
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">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> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c43">w</font></span>)</span>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T46" target="_self" title="SCMBSORT:th.46">Th46</a></i>;<br/>
<a NAME="E3:67"/><b>then </b>
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> </span>)</span> <a href="ami_1.html#K16" title="AMI_1:func.16">+*</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> 0</span>)</span> <a href="scmbsort.html#K1" title="SCMBSORT:func.1">.--&gt;</a> <font color="Maroon" title="c43">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="E4:67"/><b>then </b><i><font color="Green" title="E66">A2</font></i>: 
 <a href="scmfsa6a.html#K3" title="SCMFSA6A:func.3">Initialized</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c42">s</font>
 
<b>by </b><i><a class="txt" href="scmbsort.html#E1:67"><i><font color="Green" title="E65">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="E5:67"/>
 <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a>  is  <a href="scm_halt.html#V2" title="SCM_HALT:attr.2">InitHalting</a> <a href="scmfsa6a.html#NM1" title="SCMFSA6A:NM.1">Macro-Instruction</a>
 
<b>by </b><i><a class="ref" href="scmbsort.html#T64" target="_self" title="SCMBSORT:th.64">Th64</a></i>;<br/>
<b>hence </b><a NAME="E6:67"/>
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Computation</a> <font color="Maroon" title="c42">s</font></span>)</span> <a href="ami_1.html#K10" title="AMI_1:func.10">.</a> <font color="Maroon" title="c41">i</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <a href="scmbsort.html#K3" title="SCMBSORT:func.3">Bubble-Sort-Algorithm</a> 
 <b>by </b><i><a class="txt" href="scmbsort.html#E4:67"><i><font color="Green" title="E66">A2</font></i></a>, <a class="ref" href="scm_halt.html#D1" title="SCM_HALT:def.1">SCM_HALT:def 1</a></i>;<br/>


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