<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">i</font> be   <a href="compos_1.html#NM1" title="COMPOS_1:NM.1">Instruction</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="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> holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">i</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 ) implies  <a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font> is  <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:32"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
 for <font color="Olive" title="b1">s</font> being   <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> holds  <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">i</font>,<font color="Olive" title="b1">s</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#NK2" title="MEMSTR_0:NK.2">IC</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <font color="Olive" title="b1">s</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font> is  <a href="scmpds_4.html#V2" title="SCMPDS_4:attr.2">parahalting</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c3">m0</font> =  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font></span>)</span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">t</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-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>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="scmpds_4.html#D7" onmouseover="rs('scmpds_4/D7')" onmouseout="rh()">SCMPDS_4:def 7</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   holds <br/>(  not  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive">b<sub>1</sub></font> or <font color="Olive">b<sub>1</sub></font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">t</font> )</span><br/>

<a NAME="E2:32"/><span class="lab"><font color="Green" title="E14">A2</font></span>: 
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_1.html#K11" title="COMPOS_1:func.11">Macro</a> <font color="Maroon" title="c2">i</font>
 
;<br/>
<span class="kw">let </span><font color="Maroon" title="c5">Q</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not  <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Q</font> or <font color="Maroon" title="c5">Q</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">t</font> )</span><br/>

<span class="kw">assume </span><a NAME="E3:32"/><span class="lab"><font color="Green" title="E15">A3</font></span>: 
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c5">Q</font>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">Q</font> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c4">t</font></span><br/>

<span class="kw">take </span>
1
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="extpro_1.html#D8" onmouseover="rs('extpro_1/D8')" onmouseout="rh()">EXTPRO_1:def 8</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c4">t</font>,1)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="xtuple_0.html#K9" title="XTUPLE_0:func.9">proj1</a> <font color="Maroon" title="c5">Q</font> &amp;  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c5">Q</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c4">t</font>,1)</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> )</span><br/>

<a NAME="E4:32"/>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c4">t</font>,1)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E5:32"/>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c4">t</font>,1)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <font color="Maroon" title="c5">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partfun1.html#D2" onmouseover="rs('partfun1/D2')" onmouseout="rh()">PARTFUN1:def 2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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="c5">Q</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c4">t</font>,1)</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></span><br/>

<a NAME="E6:32"/><span class="lab"><font color="Green" title="E16">A4</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <font color="Maroon" title="c4">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#D11" onmouseover="rs('memstr_0/D11')" onmouseout="rh()">MEMSTR_0:def 11</a></span>;<br/>
<a NAME="E7:32"/><span class="kw">then </span><span class="lab"><font color="Green" title="E17">A5</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c4">t</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E13">A1</font></span></a></span>;<br/>
<a NAME="E8:32"/>
1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="compos_1.html#T57" onmouseover="rs('compos_1/T57')" onmouseout="rh()">COMPOS_1:57</a></span>;<br/>
<a NAME="E9:32"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Q</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:32"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="grfunc_1.html#T2" onmouseover="rs('grfunc_1/T2')" onmouseout="rh()">GRFUNC_1:2</a></span>;<br/>
<a NAME="E10:32"/><span class="kw">then </span><span class="lab"><font color="Green" title="E18">A6</font></span>: 
<font color="Maroon" title="c5">Q</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> 1 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="compos_1.html#T59" onmouseover="rs('compos_1/T59')" onmouseout="rh()">COMPOS_1:59</a></span>;<br/>
<a NAME="E11:32"/>
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="compos_1.html#T57" onmouseover="rs('compos_1/T57')" onmouseout="rh()">COMPOS_1:57</a></span>;<br/>
<a NAME="E12:32"/><span class="kw">then </span><span class="lab"><font color="Green" title="E19">A7</font></span>: 
<span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="compos_1.html#K9" title="COMPOS_1:func.9">Load</a> <font color="Maroon" title="c2">i</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Q</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:32"><span class="lab"><font color="Green" title="E15">A3</font></span></a>, <a class="ref" href="grfunc_1.html#T2" onmouseover="rs('grfunc_1/T2')" onmouseout="rh()">GRFUNC_1:2</a></span>;<br/>
<a NAME="E13:32"/><span class="lab"><font color="Green" title="E20">A8</font></span>: 
<font color="Maroon" title="c5">Q</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <font color="Maroon" title="c4">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">Q</font> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <font color="Maroon" title="c4">t</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" onmouseover="rs('pboole/T143')" onmouseout="rh()">PBOOLE:143</a></span>;<br/>
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c4">t</font>,<span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<font color="Maroon" title="c5">Q</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c4">t</font>,<a href="numbers.html#K5" title="NUMBERS:func.5">0</a>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" onmouseover="rs('extpro_1/T3')" onmouseout="rh()">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c4">t</font>)

<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<font color="Maroon" title="c2">i</font>,<font color="Maroon" title="c4">t</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:32"><span class="lab"><font color="Green" title="E16">A4</font></span></a>, <a class="txt" href="#E12:32"><span class="lab"><font color="Green" title="E19">A7</font></span></a>, <a class="txt" href="#E13:32"><span class="lab"><font color="Green" title="E20">A8</font></span></a>, <a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E14">A2</font></span></a>, <a class="ref" href="compos_1.html#T58" onmouseover="rs('compos_1/T58')" onmouseout="rh()">COMPOS_1:58</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E15:32"/>
 <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<font color="Maroon" title="c5">Q</font>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<font color="Maroon" title="c5">Q</font>,<font color="Maroon" title="c4">t</font>,1)</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:32"><span class="lab"><font color="Green" title="E17">A5</font></span></a>, <a class="txt" href="#E10:32"><span class="lab"><font color="Green" title="E18">A6</font></span></a>, <a class="ref" href="pboole.html#T143" onmouseover="rs('pboole/T143')" onmouseout="rh()">PBOOLE:143</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
