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<span class="kw">let </span><font color="Maroon" title="c2">P1</font>, <font color="Maroon" title="c3">P2</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s</font> being   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b2">I</font> being   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  st  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Olive" title="b2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P1</font> &amp;  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Olive" title="b2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">P2</font> holds <br/>(  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Olive" title="b1">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c3">P2</font>,<font color="Olive" title="b1">s</font>) &amp;  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P1</font>,<font color="Olive" title="b1">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P2</font>,<font color="Olive" title="b1">s</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="memstr_0.html#V4" title="MEMSTR_0:attr.4">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">I</font> being   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">Program</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>  st  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P1</font> &amp;  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Olive" title="b1">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">P2</font> holds <br/>(  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>) &amp;  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>) )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">I</font> be   <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  <a href="compos_1.html#NM5" title="COMPOS_1:NM.5">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="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c5">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P1</font> &amp;  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c5">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">P2</font> implies (  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>) &amp;  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>) ) )</span><br/>







<span class="kw">set </span><font color="Maroon" title="c6">SI</font> =  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c5">I</font>;<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:17"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
 <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c5">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">P1</font>
 <span class="kw">and </span><br/><a NAME="E2:17"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
 <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon" title="c5">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">P2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>) &amp;  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>) )</span><br/>

<a NAME="E3:17"/><span class="lab"><font color="Green" title="E10">A4</font></span>: 
<font color="Maroon" title="c3">P2</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="scmpds_4.html#D7" title="SCMPDS_4:def.7">SCMPDS_4:def 7</a></span>;<br/>
<a NAME="E4:17"/><span class="lab"><font color="Green" title="E11">A5</font></span>: 
<font color="Maroon" title="c2">P1</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="scmpds_4.html#D7" title="SCMPDS_4:def.7">SCMPDS_4:def 7</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E12">A6</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="17_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#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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c3">P2</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c7">l</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">halt</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> implies  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</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="E1:17_1"/><span class="lab"><font color="Green" title="E13">A7</font></span>: 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c3">P2</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c7">l</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K2" title="COMPOS_1:func.2">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="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</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="E2:17_1"/>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">P1</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c7">l</font>)</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c3">P2</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c7">l</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="scmpds_5.html#T16" target="_self" title="SCMPDS_5:th.16">Th20</a></span>;<br/><span class="kw">hence </span><a NAME="E3:17_1"/>
 <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</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="#E4:17"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="txt" href="#E1:17_1"><span class="lab"><font color="Green" title="E13">A7</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c3">P2</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>)</span>)</span>)</span>)</span>) = 
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c2">P1</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>)</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="scmpds_5.html#T16" target="_self" title="SCMPDS_5:th.16">Th20</a></span>
<br/>.= 
 <a href="compos_1.html#K2" title="COMPOS_1:func.2">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="#E4:17"><span class="lab"><font color="Green" title="E11">A5</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E7:17"/><span class="lab"><font color="Green" title="E13">K</font></span>: 
 <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E12">A6</font></span></a>, <a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E10">A4</font></span></a>, <a class="ref" href="extpro_1.html#D15" title="EXTPRO_1:def.15">EXTPRO_1:def 15</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>)</span><br/>

<a NAME="E8:17"/>
<font color="Maroon" title="c3">P2</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="ref" href="scmpds_4.html#D7" title="SCMPDS_4:def.7">SCMPDS_4:def 7</a></span>;<br/>
<a NAME="E9:17"/><span class="kw">then </span><span class="lab"><font color="Green" title="E14">A8</font></span>: 
 <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:17"><span class="lab"><font color="Green" title="E13">K</font></span></a>, <a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>;<br/>
<a NAME="E10:17"/>
<font color="Maroon" title="c2">P1</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">s</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="scmpds_4.html#D7" title="SCMPDS_4:def.7">SCMPDS_4:def 7</a></span>;<br/>
<a NAME="E11:17"/><span class="kw">then </span>
 <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>)</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:17"/>
 <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c2">P1</font>,<font color="Maroon" title="c4">s</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<font color="Maroon" title="c3">P2</font>,<font color="Maroon" title="c4">s</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:17"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E9:17"><span class="lab"><font color="Green" title="E14">A8</font></span></a>, <a class="ref" href="scmpds_5.html#T16" target="_self" title="SCMPDS_5:th.16">Th20</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
