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<span class="kw">let </span><font color="Maroon" title="c3">s1</font>, <font color="Maroon" title="c4">s2</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>   st <font color="Olive" title="b1">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Olive" title="b1">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c3">s1</font> &amp;  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s1</font> &amp;  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Olive" title="b1">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  holds <br/>(  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font> &amp;  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>, <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font> be   <a href="scmnorm.html#NM2" title="SCMNORM:NM.2">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c3">s1</font> &amp; <font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c3">s1</font> &amp;  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s1</font> &amp;  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s2</font> &amp; <font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  implies (  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font> &amp;  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>, <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  ) )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c6">iI</font> =  <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">I</font></span>)</span>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:26"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c3">s1</font>
 <span class="kw">and </span><br/><a NAME="E2:26"/><span class="lab"><font color="Green" title="E19">A2</font></span>: 
<font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c3">s1</font>
 <span class="kw">and </span><br/><a NAME="E3:26"/><span class="lab"><font color="Green" title="E20">A3</font></span>: 
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">s1</font>
 <span class="kw">and </span><br/><a NAME="E4:26"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
 <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">I</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">s2</font>
 <span class="kw">and </span><br/><a NAME="E5:26"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font> &amp;  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>, <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>  )</span><br/>

<a NAME="E6:26"/>
 <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K24" title="AMI_1:func.24">DataPart</a> <font color="Maroon" title="c4">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="scmpds_6.html#T4" title="SCMPDS_6:th.4">SCMPDS_6:4</a></span>;<br/>
<a NAME="E7:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A6</font></span>: 
<font color="Maroon" title="c5">I</font> <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c4">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="scmpds_6.html#T37" title="SCMPDS_6:th.37">SCMPDS_6:37</a></span>;<br/>
<a NAME="E8:26"/>
<font color="Maroon" title="c4">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s2</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></span>;<br/>
<a NAME="E9:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A7</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:26"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></span>;<br/>
<a NAME="E10:26"/>
<font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">s1</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">Initialized</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K8" title="SCMPDS_4:func.8">stop</a> <font color="Maroon" title="c5">I</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="ref" href="funct_4.html#T79" title="FUNCT_4:th.79">FUNCT_4:79</a></span>;<br/>
<a NAME="E11:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A8</font></span>: 
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c3">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E26">A9</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c7">l</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c7">l</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> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  implies  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">l</font> )</span><br/><span class="kw">assume </span><a NAME="E1:26_1"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c7">l</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> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">l</font></span><br/><a NAME="E2:26_1"/>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<font color="Maroon" title="c7">l</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<font color="Maroon" title="c7">l</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="scmpds_7.html#T26" target="_self" title="SCMPDS_7:th.26">Th26</a></span>;<br/><span class="kw">hence </span><a NAME="E3:26_1"/>
 <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c7">l</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:26"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E1:26_1"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font></span>)</span></span>)</span> = 
 <a href="ami_1.html#K7" title="AMI_1:func.7">CurInstr</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p2">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p3">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="ref" href="scmpds_7.html#T26" target="_self" title="SCMPDS_7:th.26">Th26</a></span>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:26"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E14:26"/>
 <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:26"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E9:26"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="ref" href="ami_1.html#D46" title="AMI_1:def.46">AMI_1:def 46</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>, <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> </span><br/>

<a NAME="E15:26"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A11</font></span>: 
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:26"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></span>;<br/>
<a NAME="E16:26"/>
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>,<span class="p1">(<span class="default"><a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:26"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="ami_1.html#T122" title="AMI_1:th.122">AMI_1:122</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:26"/>
 <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c3">s1</font></span>)</span>,<font color="Maroon" title="c3">s1</font>, <a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c4">s2</font></span>)</span>,<font color="Maroon" title="c4">s2</font> <a href="funct_7.html#R1" title="FUNCT_7:pred.1">equal_outside</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="txt" href="#E5:26"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E15:26"><span class="lab"><font color="Green" title="E27">A11</font></span></a>, <a class="ref" href="scmpds_7.html#T26" target="_self" title="SCMPDS_7:th.26">Th26</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
