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

<span class="kw">set </span><font color="Maroon" title="c3">i1</font> = (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>()) <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">i2</font> =  <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">WHL</font> =  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>());<br/>
<span class="kw">set </span><font color="Maroon" title="c6">pWHL</font> =  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">pI</font> =  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>();<br/>
<span class="kw">set </span><font color="Maroon" title="c8">b</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()</span>)</span>,<font color="Maroon">F<sub>6</sub></font>());<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[   <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> ] <span class="kw">means </span> for <font color="Olive" title="b1">t</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">Q</font> being   <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>  st <font color="Maroon">F<sub>1</sub></font>(<font color="Olive" title="b1">t</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> $1 &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">t</font>] &amp; <font color="Olive" title="b1">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() holds <br/>(  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Olive" title="b1">t</font>,<font color="Olive" title="b2">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Olive" title="b1">t</font>,<font color="Olive" title="b2">Q</font> );<br/>
<a NAME="E1:18_1"/><span class="lab"><font color="Green" title="E13">A5</font></span>: 
 for <font color="Olive" title="b1">k</font> being    <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>   st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c9">k</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"> ( <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font>] implies <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:18_1_1"/><span class="lab"><font color="Green" title="E14">A6</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1]</span><br/>

<span class="kw">let </span><font color="Maroon" title="c10">t</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">Q</font> being   <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>  st <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c10">t</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c10">t</font>] &amp; <font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() holds <br/>(  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Olive" title="b1">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Olive" title="b1">Q</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c10">t</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c10">t</font>] &amp; <font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() implies (  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> ) )</span><br/>



<a NAME="E2:18_1_1"/><span class="lab"><font color="Green" title="E15">T</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <font color="Maroon" title="c10">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">t</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T44" title="MEMSTR_0:th.44">MEMSTR_0:44</a></span>;<br/>
<span class="kw">assume </span><a NAME="E3:18_1_1"/><span class="lab"><font color="Green" title="E16">A7</font></span>: 
<font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c10">t</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c10">t</font>] or  not <font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() or (  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E4:18_1_1"/><span class="lab"><font color="Green" title="E17">A8</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c10">t</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() or (  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> ) )</span><br/>

<span class="kw">assume </span><a NAME="E5:18_1_1"/><span class="lab"><font color="Green" title="E18">A9</font></span>: 
<font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> )</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:18_1_1_1"/>
( <font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()</span>)</span>,<font color="Maroon">F<sub>6</sub></font>())</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()</span>)</span>,<font color="Maroon">F<sub>6</sub></font>())</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_1"/>
<font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()</span>)</span>,<font color="Maroon">F<sub>6</sub></font>())</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:18_1_1_1_1"/>
(  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18_1_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="ref" href="scmpds_8.html#T9" target="_self" title="SCMPDS_8:th.9">Th9</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_2"/><span class="lab"><font color="Green" title="E19">A10</font></span>: 
<font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()</span>)</span>,<font color="Maroon">F<sub>6</sub></font>())</span>)</span> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> )</span><br/><div class="add"><a NAME="E2:18_1_1_1_2"/><span class="lab"><font color="Green" title="E20">A14</font></span>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T36" title="COMPOS_1:th.36">COMPOS_1:36</a></span>;<br/><a NAME="E3:18_1_1_1_2"/><span class="lab"><font color="Green" title="E21">A17</font></span>: 
 <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default">(<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>()) <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span> <a href="scmpds_4.html#K2" title="SCMPDS_4:func.2">';'</a> <span class="p1">(<span class="default"><font color="Maroon">F<sub>4</sub></font>() <a href="scmpds_4.html#K3" title="SCMPDS_4:func.3">';'</a> <span class="p2">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T15" title="SCMPDS_4:th.15">SCMPDS_4:15</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c12">Q2</font> = <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c13">Q3</font> = <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c14">t4</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1);<br/><span class="kw">set </span><font color="Maroon" title="c15">Q4</font> = <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>;<br/><a NAME="E4:18_1_1_1_2"/><span class="lab"><font color="Green" title="E22">A20</font></span>: 
 <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>() <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c16">m2</font> =  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>);<br/><span class="kw">set </span><font color="Maroon" title="c17">t5</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span>);<br/><span class="kw">set </span><font color="Maroon" title="c18">Q5</font> = <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c19">l1</font> = <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/><a NAME="E5:18_1_1_1_2"/><span class="lab"><font color="Green" title="E23">A21</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c10">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#D8" title="MEMSTR_0:def.8">MEMSTR_0:def 8</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c20">m3</font> = <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1;<br/><span class="kw">set </span><font color="Maroon" title="c21">t6</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>);<br/><span class="kw">set </span><font color="Maroon" title="c22">Q6</font> = <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c23">t7</font> =  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>);<br/><span class="kw">set </span><font color="Maroon" title="c24">Q7</font> = <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>;<br/><a NAME="E6:18_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/><a NAME="E7:18_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E24">A22</font></span>: 
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_8.html#T7" target="_self" title="SCMPDS_8:th.7">Th7</a></span>;<br/><a NAME="E8:18_1_1_1_2"/><span class="lab"><font color="Green" title="E25">AA</font></span>: 
 <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a></span>;<br/><a NAME="E9:18_1_1_1_2"/>
 <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T74" title="AFINSQ_1:th.74">AFINSQ_1:74</a></span>;<br/><a NAME="E10:18_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E26">A23</font></span>: 
 <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:18_1_1_1_2"><span class="lab"><font color="Green" title="E25">AA</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><a NAME="E11:18_1_1_1_2"/>
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon">F<sub>4</sub></font>(),1) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())
 <span class="kw">by</span> <span class="lab"><a class="txt" href="scmpds_8.html#E16"><span class="lab"><font color="Green" title="E9">Lm2</font></span></a></span>;<br/><a NAME="E12:18_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E27">A24</font></span>: 
 <a href="valued_1.html#K61" title="VALUED_1:func.61">Shift</a> (<font color="Maroon">F<sub>4</sub></font>(),1) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:18_1_1_1_2"><span class="lab"><font color="Green" title="E26">A23</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/><span class="lab"><font color="Green" title="E28">A25</font></span>:  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default">(<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>()) <a href="scmpds_2.html#K10" title="SCMPDS_2:func.10">&gt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18_1_1_1_2"><span class="lab"><font color="Green" title="E21">A17</font></span></a>, <a class="ref" href="scmpds_6.html#T11" title="SCMPDS_6:th.11">SCMPDS_6:11</a>, <a class="txt" href="#E2:18_1_1"><span class="lab"><font color="Green" title="E15">T</font></span></a></span>
;<br/><a NAME="E14:18_1_1_1_2"/>
 for <font color="Olive" title="b1">a</font> being    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a>  holds  <font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Olive" title="b1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18_1_1_1_2"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a></span>;<br/><a NAME="E15:18_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E29">A27</font></span>: 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <font color="Maroon" title="c10">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#T8" title="SCMPDS_4:th.8">SCMPDS_4:8</a></span>;<br/><a NAME="E16:18_1_1_1_2"/>
<font color="Maroon">F<sub>4</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E4:18_1_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E5:18_1_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E1:18_1_1_1_2"><span class="lab"><font color="Green" title="E19">A10</font></span></a></span>;<br/><a NAME="E17:18_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E30">A28</font></span>: 
<font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c10">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a>, <a class="txt" href="#E2:18_1_1"><span class="lab"><font color="Green" title="E15">T</font></span></a></span>;<br/><a NAME="E18:18_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c10">t</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18_1_1_1_2"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="ref" href="funct_4.html#T25" title="FUNCT_4:th.25">FUNCT_4:25</a>, <a class="ref" href="funct_4.html#T98" title="FUNCT_4:th.98">FUNCT_4:98</a></span>;<br/><a NAME="E19:18_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E31">A30</font></span>: 
<font color="Maroon">F<sub>4</sub></font>() <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a>, <a class="txt" href="#E2:18_1_1"><span class="lab"><font color="Green" title="E15">T</font></span></a></span>;<br/><a NAME="E20:18_1_1_1_2"/><span class="lab"><font color="Green" title="E32">A31</font></span>: 
 <a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon" title="c11">Q</font>,<font color="Maroon" title="c10">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#D5" title="SCMPDS_4:def.5">SCMPDS_4:def 5</a></span>;<br/><a NAME="E21:18_1_1_1_2"/><span class="lab"><font color="Green" title="E33">A32</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[ <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon" title="c11">Q</font>,<font color="Maroon" title="c10">t</font>)</span>)</span>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E4:18_1_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E5:18_1_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E1:18_1_1_1_2"><span class="lab"><font color="Green" title="E19">A10</font></span></a></span>;<br/><a NAME="E22:18_1_1_1_2"/><span class="lab"><font color="Green" title="E34">A33</font></span>: 
<font color="Maroon">F<sub>4</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E4:18_1_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E5:18_1_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E1:18_1_1_1_2"><span class="lab"><font color="Green" title="E19">A10</font></span></a></span>;<br/><a NAME="E23:18_1_1_1_2"/><span class="lab"><font color="Green" title="E35">A34</font></span>: 
<font color="Maroon">F<sub>4</sub></font>() <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E4:18_1_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E5:18_1_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E1:18_1_1_1_2"><span class="lab"><font color="Green" title="E19">A10</font></span></a></span>;<br/><span class="lab"><font color="Green" title="E36">A35</font></span>:  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span> = 
 <a href="ordinal1.html#K1" title="ORDINAL1:func.1">succ</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <font color="Maroon" title="c10">t</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1_1_2"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="txt" href="#E13:18_1_1_1_2"><span class="lab"><font color="Green" title="E28">A25</font></span></a>, <a class="ref" href="scmpds_2.html#T57" title="SCMPDS_2:th.57">SCMPDS_2:57</a>, <a class="txt" href="#E5:18_1_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a></span>
<br/>.= 
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18_1_1_1_2"><span class="lab"><font color="Green" title="E23">A21</font></span></a></span>
;<br/><a NAME="E25:18_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A36</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:18_1_1_1_2"><span class="lab"><font color="Green" title="E22">A20</font></span></a>, <a class="txt" href="#E19:18_1_1_1_2"><span class="lab"><font color="Green" title="E31">A30</font></span></a>, <a class="txt" href="#E23:18_1_1_1_2"><span class="lab"><font color="Green" title="E35">A34</font></span></a>, <a class="txt" href="#E15:18_1_1_1_2"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="txt" href="#E12:18_1_1_1_2"><span class="lab"><font color="Green" title="E27">A24</font></span></a>, <a class="ref" href="scmpds_7.html#T18" title="SCMPDS_7:th.18">SCMPDS_7:18</a></span>;<br/><a NAME="E26:18_1_1_1_2"/><span class="lab"><font color="Green" title="E38">A37</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" title="PBOOLE:th.143">PBOOLE:143</a></span>;<br/><a NAME="E27:18_1_1_1_2"/><span class="lab"><font color="Green" title="E39">A38</font></span>: 
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A39</font></span>:  <a href="extpro_1.html#K3" title="EXTPRO_1:func.3">CurInstr</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span> <a href="compos_1.html#K3" title="COMPOS_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:18_1_1_1_2"><span class="lab"><font color="Green" title="E22">A20</font></span></a>, <a class="txt" href="#E19:18_1_1_1_2"><span class="lab"><font color="Green" title="E31">A30</font></span></a>, <a class="txt" href="#E23:18_1_1_1_2"><span class="lab"><font color="Green" title="E35">A34</font></span></a>, <a class="txt" href="#E24:18_1_1_1_2"><span class="lab"><font color="Green" title="E36">A35</font></span></a>, <a class="txt" href="#E15:18_1_1_1_2"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="txt" href="#E12:18_1_1_1_2"><span class="lab"><font color="Green" title="E27">A24</font></span></a>, <a class="txt" href="#E26:18_1_1_1_2"><span class="lab"><font color="Green" title="E38">A37</font></span></a>, <a class="ref" href="scmpds_7.html#T18" title="SCMPDS_7:th.18">SCMPDS_7:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18_1_1_1_2"><span class="lab"><font color="Green" title="E24">A22</font></span></a>, <a class="txt" href="#E10:18_1_1_1_2"><span class="lab"><font color="Green" title="E26">A23</font></span></a>, <a class="ref" href="grfunc_1.html#T2" title="GRFUNC_1:th.2">GRFUNC_1:2</a></span>
<br/>.= 
 <a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p1">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_8.html#T8" target="_self" title="SCMPDS_8:th.8">Th8</a></span>
;<br/><span class="lab"><font color="Green" title="E41">A41</font></span>:  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" title="EXTPRO_1:th.3">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:18_1_1_1_2"><span class="lab"><font color="Green" title="E40">A39</font></span></a></span>
;<br/><span class="kw">then </span> <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> = 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> (<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</a></span>
<br/>.= 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:18_1_1_1_2"><span class="lab"><font color="Green" title="E37">A36</font></span></a>, <a class="txt" href="#E27:18_1_1_1_2"><span class="lab"><font color="Green" title="E39">A38</font></span></a>, <a class="ref" href="scmpds_7.html#T1" title="SCMPDS_7:th.1">SCMPDS_7:1</a></span>
;<br/><a NAME="E31:18_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E42">A42</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T46" title="MEMSTR_0:th.46">MEMSTR_0:46</a></span>;<br/><a NAME="E32:18_1_1_1_2"/><span class="lab"><font color="Green" title="E43">A43</font></span>: 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:18_1_1_1_2"><span class="lab"><font color="Green" title="E22">A20</font></span></a>, <a class="txt" href="#E19:18_1_1_1_2"><span class="lab"><font color="Green" title="E31">A30</font></span></a>, <a class="txt" href="#E23:18_1_1_1_2"><span class="lab"><font color="Green" title="E35">A34</font></span></a>, <a class="txt" href="#E24:18_1_1_1_2"><span class="lab"><font color="Green" title="E36">A35</font></span></a>, <a class="txt" href="#E15:18_1_1_1_2"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="txt" href="#E12:18_1_1_1_2"><span class="lab"><font color="Green" title="E27">A24</font></span></a>, <a class="ref" href="scmpds_7.html#T18" title="SCMPDS_7:th.18">SCMPDS_7:18</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E44">A44</font></span>:  <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span>)</span>)</span> = 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18_1_1_1_2"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>
<br/>.= 
 <a href="memstr_0.html#K4" title="MEMSTR_0:func.4">DataPart</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon" title="c11">Q</font>,<font color="Maroon" title="c10">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_4.html#D5" title="SCMPDS_4:def.5">SCMPDS_4:def 5</a></span>
;<br/><a NAME="E34:18_1_1_1_2"/>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T12" title="SCMPDS_2:th.12">SCMPDS_2:12</a></span>;<br/><a NAME="E35:18_1_1_1_2"/><span class="kw">then </span>
 <a href="compos_1.html#K5" title="COMPOS_1:func.5">InsCode</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K4" title="SCMPDS_2:func.4">goto</a> <span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K9" title="DOMAIN_1:func.9">{</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,4,5,6</span><a href="domain_1.html#K9" title="DOMAIN_1:func.9">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D2" title="ENUMSET1:def.2">ENUMSET1:def 2</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A45</font></span>:  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> = 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:18_1_1_1_2"><span class="lab"><font color="Green" title="E41">A41</font></span></a>, <a class="ref" href="scmpds_8.html#T3" target="_self" title="SCMPDS_8:th.3">Th3</a></span>
<br/>.= 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon" title="c11">Q</font>,<font color="Maroon" title="c10">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:18_1_1_1_2"><span class="lab"><font color="Green" title="E44">A44</font></span></a>, <a class="txt" href="#E27:18_1_1_1_2"><span class="lab"><font color="Green" title="E39">A38</font></span></a>, <a class="ref" href="memstr_0.html#T80" title="MEMSTR_0:th.80">MEMSTR_0:80</a></span>
;<br/><div><span class="lab"><font color="Green" title="E46">A46</font></span>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1_1_2_8"><span class="kw">now </span></a><div class="add"><a NAME="E1:18_1_1_1_2_8"/>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="scmpds_4.html#K6" title="SCMPDS_4:func.6">IExec</a> (<font color="Maroon">F<sub>4</sub></font>(),<font color="Maroon" title="c11">Q</font>,<font color="Maroon" title="c10">t</font>)</span>)</span></span>)</span>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c10">t</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E4:18_1_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E5:18_1_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E1:18_1_1_1_2"><span class="lab"><font color="Green" title="E19">A10</font></span></a></span>;<br/><a NAME="E2:18_1_1_1_2_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A47</font></span>: 
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18_1_1"><span class="lab"><font color="Green" title="E16">A7</font></span></a>, <a class="txt" href="#E36:18_1_1_1_2"><span class="lab"><font color="Green" title="E45">A45</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><span class="kw">assume </span><a NAME="E3:18_1_1_1_2_8"/>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="memstr_0.html#K6" title="MEMSTR_0:func.6">Initialize</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p0">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span></span>)</span>) <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> <font color="Maroon" title="c9">k</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">hence </span><a NAME="E4:18_1_1_1_2_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_1_1_1_2_8"><span class="lab"><font color="Green" title="E47">A47</font></span></a>, <a class="ref" href="int_1.html#T7" title="INT_1:th.7">INT_1:7</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><span class="lab"><font color="Green" title="E47">A48</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:18_1_1_1_2"><span class="lab"><font color="Green" title="E43">A43</font></span></a>, <a class="ref" href="scmpds_4.html#T8" title="SCMPDS_4:th.8">SCMPDS_4:8</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="extpro_1.html#K6" title="EXTPRO_1:func.6">Result</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:18_1_1_1_2"><span class="lab"><font color="Green" title="E30">A28</font></span></a>, <a class="ref" href="extpro_1.html#T23" title="EXTPRO_1:th.23">EXTPRO_1:23</a></span>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:18_1_1"><span class="lab"><font color="Green" title="E18">A9</font></span></a>, <a class="txt" href="#E3:18"><span class="lab"><font color="Green" title="E12">A4</font></span></a>, <a class="txt" href="#E4:18_1_1"><span class="lab"><font color="Green" title="E17">A8</font></span></a>, <a class="txt" href="#E1:18_1_1_1_2"><span class="lab"><font color="Green" title="E19">A10</font></span></a>, <a class="txt" href="#E20:18_1_1_1_2"><span class="lab"><font color="Green" title="E32">A31</font></span></a></span>
;<br/><span class="lab"><font color="Green" title="E48">A50</font></span>: <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() = 
<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:18_1_1_1_2"><span class="lab"><font color="Green" title="E41">A41</font></span></a>, <a class="ref" href="scmpds_2.html#T54" title="SCMPDS_2:th.54">SCMPDS_2:54</a></span>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:18_1_1_1_2"><span class="lab"><font color="Green" title="E47">A48</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>
;<br/><a NAME="E40:18_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E49">A51</font></span>: 
 <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>),<font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E21:18_1_1_1_2"><span class="lab"><font color="Green" title="E33">A32</font></span></a>, <a class="txt" href="#E36:18_1_1_1_2"><span class="lab"><font color="Green" title="E45">A45</font></span></a>, <a class="txt" href="#E37:18_1_1_1_2"><span class="lab"><font color="Green" title="E46">A46</font></span></a>, <a class="txt" href="#E31:18_1_1_1_2"><span class="lab"><font color="Green" title="E42">A42</font></span></a></span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_1_1_2_11"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c25">k</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="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2_11_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:18_1_1_1_2_11_1"/>
( <font color="Maroon" title="c25">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 or <font color="Maroon" title="c25">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2_11_1_1"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_2_11_1_1"/>
<font color="Maroon" title="c25">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:18_1_1_1_2_11_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A52</font></span>: 
<font color="Maroon" title="c25">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T7" title="INT_1:th.7">INT_1:7</a></span>;<br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2_11_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:18_1_1_1_2_11_1_1_1_1"/>
( <font color="Maroon" title="c25">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>) or <font color="Maroon" title="c25">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_1_1_1_2_11_1_1"><span class="lab"><font color="Green" title="E50">A52</font></span></a>, <a class="ref" href="nat_1.html#T8" title="NAT_1:th.8">NAT_1:8</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2_11_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_2_11_1_1_1_1_1"/><span class="lab"><font color="Green" title="E51">A53</font></span>: 
<font color="Maroon" title="c25">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span><br/><div class="add"><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2_11_1_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:18_1_1_1_2_11_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c25">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c25">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2_11_1_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_2_11_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c25">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:18_1_1_1_2_11_1_1_1_1_1_1_1_1"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18_1_1_1_2"><span class="lab"><font color="Green" title="E20">A14</font></span></a>, <a class="txt" href="#E5:18_1_1_1_2"><span class="lab"><font color="Green" title="E23">A21</font></span></a>, <a class="ref" href="extpro_1.html#T2" title="EXTPRO_1:th.2">EXTPRO_1:2</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2_11_1_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c25">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">kn</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E52">A54</font></span>: 
<font color="Maroon" title="c25">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c26">kn</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T6" title="NAT_1:th.6">NAT_1:6</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c27">kn</font> = <font color="Maroon" title="c26">kn</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c28">lm</font> =  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c27">kn</font>)</span>)</span> as    <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>  ;<br/><a NAME="E6:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c27">kn</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c25">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18_1_1_1_2_11_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A54</font></span></a>, <a class="ref" href="xreal_1.html#T29" title="XREAL_1:th.29">XREAL_1:29</a></span>;<br/><a NAME="E7:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c27">kn</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1_1_2_11_1_1_1_1_1"><span class="lab"><font color="Green" title="E51">A53</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E8:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c27">kn</font>)</span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,1)</span>)</span>,<font color="Maroon" title="c27">kn</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:18_1_1_1_2"><span class="lab"><font color="Green" title="E22">A20</font></span></a>, <a class="txt" href="#E19:18_1_1_1_2"><span class="lab"><font color="Green" title="E31">A30</font></span></a>, <a class="txt" href="#E23:18_1_1_1_2"><span class="lab"><font color="Green" title="E35">A34</font></span></a>, <a class="txt" href="#E24:18_1_1_1_2"><span class="lab"><font color="Green" title="E36">A35</font></span></a>, <a class="txt" href="#E15:18_1_1_1_2"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="txt" href="#E12:18_1_1_1_2"><span class="lab"><font color="Green" title="E27">A24</font></span></a>, <a class="ref" href="scmpds_7.html#T16" title="SCMPDS_7:th.16">SCMPDS_7:16</a></span>;<br/><a NAME="E9:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A56</font></span>: 
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c28">lm</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18_1_1_1_2_11_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A54</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>;<br/><a NAME="E10:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c27">kn</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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E22:18_1_1_1_2"><span class="lab"><font color="Green" title="E34">A33</font></span></a>, <a class="ref" href="scmpds_6.html#D2" title="SCMPDS_6:def.2">SCMPDS_6:def 2</a>, <a class="txt" href="#E2:18_1_1"><span class="lab"><font color="Green" title="E15">T</font></span></a></span>;<br/><a NAME="E11:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c28">lm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</a></span>;<br/><a NAME="E12:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c28">lm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#T55" title="COMPOS_1:th.55">COMPOS_1:55</a></span>;<br/><a NAME="E13:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A57</font></span>: 
<font color="Maroon" title="c28">lm</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T7" title="INT_1:th.7">INT_1:7</a></span>;<br/><a NAME="E14:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/><a NAME="E15:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c28">lm</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:18_1_1_1_2_11_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E54">A57</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/><a NAME="E16:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c28">lm</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="scmpds_8.html#E9"><span class="lab"><font color="Green" title="E4">Lm1</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E17:18_1_1_1_2_11_1_1_1_1_1_1_1_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:18_1_1_1_2_11_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A56</font></span></a>, <a class="ref" href="afinsq_1.html#T66" title="AFINSQ_1:th.66">AFINSQ_1:66</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></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2_11_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_2_11_1_1_1_1_2"/><span class="lab"><font color="Green" title="E51">A58</font></span>: 
<font color="Maroon" title="c25">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span><br/><div class="add"><a NAME="E2:18_1_1_1_2_11_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:18_1_1_1_2"><span class="lab"><font color="Green" title="E24">A22</font></span></a>, <a class="ref" href="compos_1.html#T62" title="COMPOS_1:th.62">COMPOS_1:62</a></span>;<br/><span class="kw">hence </span><a NAME="E3:18_1_1_1_2_11_1_1_1_1_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:18_1_1_1_2"><span class="lab"><font color="Green" title="E22">A20</font></span></a>, <a class="txt" href="#E19:18_1_1_1_2"><span class="lab"><font color="Green" title="E31">A30</font></span></a>, <a class="txt" href="#E23:18_1_1_1_2"><span class="lab"><font color="Green" title="E35">A34</font></span></a>, <a class="txt" href="#E24:18_1_1_1_2"><span class="lab"><font color="Green" title="E36">A35</font></span></a>, <a class="txt" href="#E15:18_1_1_1_2"><span class="lab"><font color="Green" title="E29">A27</font></span></a>, <a class="txt" href="#E12:18_1_1_1_2"><span class="lab"><font color="Green" title="E27">A24</font></span></a>, <a class="txt" href="#E27:18_1_1_1_2"><span class="lab"><font color="Green" title="E39">A38</font></span></a>, <a class="txt" href="#E1:18_1_1_1_2_11_1_1_1_1_2"><span class="lab"><font color="Green" title="E51">A58</font></span></a>, <a class="ref" href="scmpds_7.html#T18" title="SCMPDS_7:th.18">SCMPDS_7:18</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></div><span class="kw">end;</span></div></div>
<span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="18_1_1_1_2_11_1_2"><span class="kw">suppose </span></a><a NAME="E1:18_1_1_1_2_11_1_2"/>
<font color="Maroon" title="c25">k</font> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p3">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p4">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Olive">b<sub>1</sub></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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c26">nn</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:18_1_1_1_2_11_1_2"/><span class="lab"><font color="Green" title="E50">A59</font></span>: 
<font color="Maroon" title="c25">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c26">nn</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" title="NAT_1:th.10">NAT_1:10</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c27">nn</font> = <font color="Maroon" title="c26">nn</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/><a NAME="E5:18_1_1_1_2_11_1_2"/>
<font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T93" title="FUNCT_4:th.93">FUNCT_4:93</a></span>;<br/><a NAME="E6:18_1_1_1_2_11_1_2"/><span class="kw">then </span>
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p5">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p0">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)</span>)</span>,<font color="Maroon" title="c27">nn</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18_1_1_1_2_11_1_2"><span class="lab"><font color="Green" title="E50">A59</font></span></a>, <a class="ref" href="extpro_1.html#T4" title="EXTPRO_1:th.4">EXTPRO_1:4</a></span>;<br/><span class="kw">hence </span><a NAME="E7:18_1_1_1_2_11_1_2"/>
 <a href="memstr_0.html#K3" title="MEMSTR_0:func.3">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p3">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c25">k</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> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E40:18_1_1_1_2"><span class="lab"><font color="Green" title="E49">A51</font></span></a>, <a class="ref" href="scmpds_6.html#D2" title="SCMPDS_6:def.2">SCMPDS_6:def 2</a>, <a class="txt" href="#E31:18_1_1_1_2"><span class="lab"><font color="Green" title="E42">A42</font></span></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></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E42:18_1_1_1_2"/>
 <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#D2" title="SCMPDS_6:def.2">SCMPDS_6:def 2</a>, <a class="txt" href="#E2:18_1_1"><span class="lab"><font color="Green" title="E15">T</font></span></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="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font></span><br/><a NAME="E43:18_1_1_1_2"/><span class="lab"><font color="Green" title="E50">RR</font></span>: 
<font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T93" title="FUNCT_4:th.93">FUNCT_4:93</a></span>;<br/><a NAME="E44:18_1_1_1_2"/>
 <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>),<font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_1"><span class="lab"><font color="Green" title="E14">A6</font></span></a>, <a class="txt" href="#E21:18_1_1_1_2"><span class="lab"><font color="Green" title="E33">A32</font></span></a>, <a class="txt" href="#E39:18_1_1_1_2"><span class="lab"><font color="Green" title="E48">A50</font></span></a>, <a class="txt" href="#E36:18_1_1_1_2"><span class="lab"><font color="Green" title="E45">A45</font></span></a>, <a class="txt" href="#E37:18_1_1_1_2"><span class="lab"><font color="Green" title="E46">A46</font></span></a>, <a class="txt" href="#E31:18_1_1_1_2"><span class="lab"><font color="Green" title="E42">A42</font></span></a></span>;<br/><a NAME="E45:18_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a>  <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="extpro_1.html#K8" title="EXTPRO_1:func.8">LifeSpan</a> (<span class="p4">(<span class="default"><font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p5">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:18_1_1_1_2"><span class="lab"><font color="Green" title="E42">A42</font></span></a>, <a class="txt" href="#E43:18_1_1_1_2"><span class="lab"><font color="Green" title="E50">RR</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="E46:18_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c11">Q</font> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="compos_1.html#K15" title="COMPOS_1:func.15">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>())</span>)</span></span>)</span> <a href="extpro_1.html#R1" title="EXTPRO_1:pred.1">halts_on</a> <font color="Maroon" title="c10">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T22" title="EXTPRO_1:th.22">EXTPRO_1:22</a></span>;<br/><span class="kw">hence </span><a NAME="E47:18_1_1_1_2"/>
 <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_6.html#D3" title="SCMPDS_6:def.3">SCMPDS_6:def 3</a>, <a class="txt" href="#E2:18_1_1"><span class="lab"><font color="Green" title="E15">T</font></span></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></div><span class="kw">end;</span></div>

</div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c9">n</font> = <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">F<sub>2</sub></font>());<br/>
<a NAME="E2:18_1"/><span class="lab"><font color="Green" title="E14">A60</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c10">t</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">Q</font> being   <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>  st <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c10">t</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c10">t</font>] &amp; <font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() holds <br/>(  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Olive" title="b1">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Olive" title="b1">Q</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">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" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c10">t</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c10">t</font>] &amp; <font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() implies (  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> ) )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:18_1_2"/><span class="lab"><font color="Green" title="E15">A61</font></span>: 
<font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c10">t</font>) <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <span class="kw">and </span><br/><a NAME="E2:18_1_2"/><span class="lab"><font color="Green" title="E16">A62</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c10">t</font>]
 <span class="kw">and </span><br/><a NAME="E3:18_1_2"/><span class="lab"><font color="Green" title="E17">A63</font></span>: 
<font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>() <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> )</span><br/>

<a NAME="E4:18_1_2"/>
<font color="Maroon">F<sub>1</sub></font>(<font color="Maroon" title="c10">t</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18_1_2"><span class="lab"><font color="Green" title="E15">A61</font></span></a></span>;<br/>
<a NAME="E5:18_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">t</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon">F<sub>5</sub></font>()</span>)</span>,<font color="Maroon">F<sub>6</sub></font>())</span>)</span> <a href="xxreal_0.html#NR2" title="XXREAL_0:NR.2">&gt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:18"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="txt" href="#E2:18_1_2"><span class="lab"><font color="Green" title="E16">A62</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:18_1_2"/>
(  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon" title="c10">t</font>,<font color="Maroon" title="c11">Q</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:18_1_2"><span class="lab"><font color="Green" title="E17">A63</font></span></a>, <a class="ref" href="scmpds_8.html#T9" target="_self" title="SCMPDS_8:th.9">Th9</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 NAME="E3:18_1"/>
 for <font color="Olive" title="b1">k</font> being    <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>  holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>]
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="nat_1.html#S1" title="NAT_1:sch.1">NAT_1:sch 1</a>(<a class="txt" href="#E2:18_1"><span class="lab"><font color="Green" title="E14">A60</font></span></a>, <a class="txt" href="#E1:18_1"><span class="lab"><font color="Green" title="E13">A5</font></span></a>);<br/></span>
<a NAME="E4:18_1"/><span class="kw">then </span>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">F<sub>1</sub></font>(<font color="Maroon">F<sub>2</sub></font>())]
 
;<br/>
<span class="kw">hence </span><a NAME="E5:18_1"/>
(  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R1" title="SCMPDS_6:pred.1">is_closed_on</a> <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() &amp;  <a href="scmpds_8.html#K1" title="SCMPDS_8:func.1">while&lt;0</a> (<font color="Maroon">F<sub>5</sub></font>(),<font color="Maroon">F<sub>6</sub></font>(),<font color="Maroon">F<sub>4</sub></font>()) <a href="scmpds_6.html#R2" title="SCMPDS_6:pred.2">is_halting_on</a> <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon">F<sub>3</sub></font>() )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:18"><span class="lab"><font color="Green" title="E11">A3</font></span></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>
