<?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#K8" title="SCMPDS_2:func.8">&lt;=0_goto</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">i2</font> =  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">WHL</font> =  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K10" title="COMPOS_1:func.10">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#K2" title="SCMPDS_2:func.2">DataLoc</a> (<span class="p1">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>] <span class="kw">means </span> for <font color="Olive" title="b1">t</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><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="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() holds <br/>(  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K2" title="SCMPDS_8:func.2">while&gt;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="E1:36_1"/><span class="lab"><font color="Green" title="E21">A4</font></span>: 
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#K1" title="NAT_1:func.1">+</a> 1]
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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#K1" title="NAT_1:func.1">+</a> 1] )</span><br/>

<span class="kw">assume </span><a NAME="E1:36_1_1"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font>]
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]</span><br/>

<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_1_1_1"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">t</font> being   <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a><br/>  for <font color="Olive" title="b2">Q</font>, <font color="Olive" title="b3">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> <font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() holds <br/>(  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="b3">Q</font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="b3">Q</font> )</span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c10">t</font> be   <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">Q</font>, <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="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#K1" title="NAT_1:func.1">+</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="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() holds <br/>(  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>3</sub></font>,<font color="Olive">b<sub>5</sub></font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>3</sub></font>,<font color="Olive">b<sub>5</sub></font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c11">Q</font>, <font color="Maroon" title="c12">Q</font> be   <a href="compos_1.html#NM2" title="COMPOS_1:NM.2">Instruction-Sequence</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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#K1" title="NAT_1:func.1">+</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="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() implies (  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> ) )</span><br/><span class="kw">assume </span><a NAME="E1:36_1_1_1"/><span class="lab"><font color="Green" title="E23">A6</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#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <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="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() implies (  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> ) )</span><br/><span class="kw">assume </span><a NAME="E2:36_1_1_1"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c10">t</font>]
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c10">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() implies (  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> ) )</span><br/><span class="kw">assume </span><a NAME="E3:36_1_1_1"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
<font color="Maroon" title="c10">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>()
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> )</span><br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_1_1_1"/>
( <font color="Maroon" title="c10">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c10">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_1_1"/>
<font color="Maroon" title="c10">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:36_1_1_1_1_1"/>
(  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">Q</font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">Q</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="scmpds_8.html#T20" target="_self" onmouseover="rs('scmpds_8/T20')" onmouseout="rh()">Th18</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
<font color="Maroon" title="c10">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> &amp;  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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">b<sub>1</sub></font>,<font color="Olive">b<sub>3</sub></font> )</span><br/><div class="add"><a NAME="E2:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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" onmouseover="rs('compos_1/T36')" onmouseout="rh()">COMPOS_1:36</a></span>;<br/><a NAME="E3:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
 <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K8" title="SCMPDS_2:func.8">&lt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K3" title="SCMPDS_2:func.3">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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" onmouseover="rs('scmpds_4/T15')" onmouseout="rh()">SCMPDS_4:15</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c13">t2</font> = <font color="Maroon" title="c10">t</font>;<br/><span class="kw">set </span><font color="Maroon" title="c14">Q2</font> = <font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>;<br/><span class="kw">set </span><font color="Maroon" title="c15">t3</font> = <font color="Maroon" title="c10">t</font>;<br/><span class="kw">set </span><font color="Maroon" title="c16">Q3</font> = <font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c17">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c18">Q4</font> = <font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="E4:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">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="c12">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#K10" title="COMPOS_1:func.10">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" onmouseover="rs('funct_4/T25')" onmouseout="rh()">FUNCT_4:25</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c19">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="c12">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#K10" title="COMPOS_1:func.10">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="c20">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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="c21">Q5</font> = <font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c22">l1</font> = <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/><a NAME="E5:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E30">A13</font></span>: 
 <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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" onmouseover="rs('memstr_0/T44')" onmouseout="rh()">MEMSTR_0:44</a></span>;<br/><a NAME="E6:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <font color="Maroon" title="c10">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#D11" onmouseover="rs('memstr_0/D11')" onmouseout="rh()">MEMSTR_0:def 11</a></span>;<br/><span class="kw">set </span><font color="Maroon" title="c23">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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1;<br/><span class="kw">set </span><font color="Maroon" title="c24">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span>);<br/><span class="kw">set </span><font color="Maroon" title="c25">Q6</font> = <font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c26">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>);<br/><span class="kw">set </span><font color="Maroon" title="c27">Q7</font> = <font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="E7:36_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>;<br/><a NAME="E8:36_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E32">A15</font></span>: 
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#T18" target="_self" onmouseover="rs('scmpds_8/T18')" onmouseout="rh()">Th16</a></span>;<br/><a NAME="E9:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E33">A16</font></span>: 
 <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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" onmouseover="rs('afinsq_1/T74')" onmouseout="rh()">AFINSQ_1:74</a></span>;<br/><a NAME="E10:36_1_1_1_1_2"/>
 <a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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" onmouseover="rs('funct_4/T25')" onmouseout="rh()">FUNCT_4:25</a></span>;<br/><a NAME="E11:36_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E34">A17</font></span>: 
 <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="#E9:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/><a NAME="E12:36_1_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#K2" title="SCMPDS_8:func.2">while&gt;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#E30"><span class="lab"><font color="Green" title="E17">Lm4</font></span></a></span>;<br/><a NAME="E13:36_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A18</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="#E11:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="ref" href="xboole_1.html#T1" onmouseover="rs('xboole_1/T1')" onmouseout="rh()">XBOOLE_1:1</a></span>;<br/><span class="lab"><font color="Green" title="E36">A19</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K5" title="NUMBERS:func.5">0</a>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" onmouseover="rs('extpro_1/T3')" onmouseout="rh()">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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>)

<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#K8" title="SCMPDS_2:func.8">&lt;=0_goto</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="#E3:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E5:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="scmpds_6.html#T11" onmouseover="rs('scmpds_6/T11')" onmouseout="rh()">SCMPDS_6:11</a></span>
;<br/><a NAME="E15:36_1_1_1_1_2"/>
 for <font color="Olive" title="b1">a</font> being   <a href="scmpds_2.html#NM1" title="SCMPDS_2:NM.1">Int_position</a> holds  <font color="Maroon" title="c10">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="ref" href="scmpds_2.html#T56" onmouseover="rs('scmpds_2/T56')" onmouseout="rh()">SCMPDS_2:56</a></span>;<br/><a NAME="E16:36_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A20</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">DataPart</a> <font color="Maroon" title="c10">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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" onmouseover="rs('scmpds_4/T8')" onmouseout="rh()">SCMPDS_4:8</a></span>;<br/><a NAME="E17:36_1_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="c12">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E2:36_1_1_1"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E1:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E26">A9</font></span></a></span>;<br/><a NAME="E18:36_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E38">A21</font></span>: 
<font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">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="#E5:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="scmpds_6.html#D3" onmouseover="rs('scmpds_6/D3')" onmouseout="rh()">SCMPDS_6:def 3</a></span>;<br/><a NAME="E19:36_1_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">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#K10" title="COMPOS_1:func.10">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="#E18:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E38">A21</font></span></a></span>;<br/><a NAME="E20:36_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E39">A22</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="scmpds_6.html#D3" onmouseover="rs('scmpds_6/D3')" onmouseout="rh()">SCMPDS_6:def 3</a></span>;<br/><a NAME="E21:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E40">A23</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="c12">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="c12">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#K10" title="COMPOS_1:func.10">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" onmouseover="rs('scmpds_4/D5')" onmouseout="rh()">SCMPDS_4:def 5</a></span>;<br/><a NAME="E22:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E41">A24</font></span>: 
<font color="Maroon">P<sub>1</sub></font>[ <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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="c12">Q</font>,<font color="Maroon" title="c10">t</font>)</span>)</span>]
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E2:36_1_1_1"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E1:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E26">A9</font></span></a></span>;<br/><a NAME="E23:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E42">A25</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="c12">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E2:36_1_1_1"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E1:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E26">A9</font></span></a></span>;<br/><a NAME="E24:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E43">A26</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E2:36_1_1_1"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E1:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E26">A9</font></span></a></span>;<br/><span class="lab"><font color="Green" title="E44">A27</font></span>:  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <font color="Maroon" title="c10">t</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E14:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E36">A19</font></span></a>, <a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="ref" href="scmpds_2.html#T56" onmouseover="rs('scmpds_2/T56')" onmouseout="rh()">SCMPDS_2:56</a></span>
<br/>.= 
<a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E31">A14</font></span></a></span>
;<br/><a NAME="E26:36_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A28</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E20:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E24:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E16:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E13:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="ref" href="scmpds_7.html#T18" onmouseover="rs('scmpds_7/T18')" onmouseout="rh()">SCMPDS_7:18</a></span>;<br/><a NAME="E27:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E46">A29</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K5" title="MEMSTR_0:func.5">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K5" title="MEMSTR_0:func.5">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T143" onmouseover="rs('pboole/T143')" onmouseout="rh()">PBOOLE:143</a></span>;<br/><a NAME="E28:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E47">A30</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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" onmouseover="rs('extpro_1/T4')" onmouseout="rh()">EXTPRO_1:4</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A31</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span>) = 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E20:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E24:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E25:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="txt" href="#E16:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E13:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="txt" href="#E27:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E46">A29</font></span></a>, <a class="ref" href="scmpds_7.html#T18" onmouseover="rs('scmpds_7/T18')" onmouseout="rh()">SCMPDS_7:18</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="txt" href="#E11:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E34">A17</font></span></a>, <a class="ref" href="grfunc_1.html#T2" onmouseover="rs('grfunc_1/T2')" onmouseout="rh()">GRFUNC_1:2</a></span>
<br/>.= 
 <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_8.html#T19" target="_self" onmouseover="rs('scmpds_8/T19')" onmouseout="rh()">Th17</a></span>
;<br/><span class="lab"><font color="Green" title="E49">A32</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) = 
 <a href="extpro_1.html#K4" title="EXTPRO_1:func.4">Following</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="extpro_1.html#T3" onmouseover="rs('extpro_1/T3')" onmouseout="rh()">EXTPRO_1:3</a></span>
<br/>.= 
 <a href="extpro_1.html#K2" title="EXTPRO_1:func.2">Exec</a> (<span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E48">A31</font></span></a></span>
;<br/><span class="kw">then </span> <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> = 
 <a href="scmpds_2.html#K17" title="SCMPDS_2:func.17">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T54" onmouseover="rs('scmpds_2/T54')" onmouseout="rh()">SCMPDS_2:54</a></span>
<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E26:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E45">A28</font></span></a>, <a class="txt" href="#E28:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E47">A30</font></span></a>, <a class="ref" href="scmpds_7.html#T1" onmouseover="rs('scmpds_7/T1')" onmouseout="rh()">SCMPDS_7:1</a></span>
;<br/><a NAME="E32:36_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A33</font></span>: 
 <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="memstr_0.html#T46" onmouseover="rs('memstr_0/T46')" onmouseout="rh()">MEMSTR_0:46</a></span>;<br/><a NAME="E33:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E51">A34</font></span>: 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">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="c12">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#K10" title="COMPOS_1:func.10">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="c12">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#K10" title="COMPOS_1:func.10">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#K6" title="MEMSTR_0:func.6">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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="#E4:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E20:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E24:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E25:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="txt" href="#E16:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E13:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="ref" href="scmpds_7.html#T18" onmouseover="rs('scmpds_7/T18')" onmouseout="rh()">SCMPDS_7:18</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A35</font></span>:  <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K6" title="MEMSTR_0:func.6">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="c12">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#K10" title="COMPOS_1:func.10">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="#E18:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="ref" href="extpro_1.html#T23" onmouseover="rs('extpro_1/T23')" onmouseout="rh()">EXTPRO_1:23</a></span>
<br/>.= 
 <a href="memstr_0.html#K6" title="MEMSTR_0:func.6">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="c12">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" onmouseover="rs('scmpds_4/D5')" onmouseout="rh()">SCMPDS_4:def 5</a></span>
;<br/><a NAME="E35:36_1_1_1_1_2"/>
 <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 14
 <span class="kw">by</span> <span class="lab"><a class="ref" href="scmpds_2.html#T12" onmouseover="rs('scmpds_2/T12')" onmouseout="rh()">SCMPDS_2:12</a></span>;<br/><a NAME="E36:36_1_1_1_1_2"/><span class="kw">then </span>
 <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"><a href="domain_1.html#K10" title="DOMAIN_1:func.10">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">0</a>,4,5,6,14</span><a href="domain_1.html#K10" title="DOMAIN_1:func.10">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="enumset1.html#D3" onmouseover="rs('enumset1/D3')" onmouseout="rh()">ENUMSET1:def 3</a></span>;<br/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A36</font></span>:  <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> = 
 <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="ref" href="scmpds_8.html#T3" target="_self" onmouseover="rs('scmpds_8/T3')" onmouseout="rh()">Th2</a></span>
<br/>.= 
 <a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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="c12">Q</font>,<font color="Maroon" title="c10">t</font>)</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E34:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E52">A35</font></span></a>, <a class="txt" href="#E28:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E47">A30</font></span></a>, <a class="ref" href="memstr_0.html#T80" onmouseover="rs('memstr_0/T80')" onmouseout="rh()">MEMSTR_0:80</a></span>
;<br/><div><span class="lab"><font color="Green" title="E54">A37</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_1_1_1_1_2_8"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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></span></a><div class="add"><a NAME="E1:36_1_1_1_1_2_8"/>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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="c12">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>(<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">Initialize</a> <font color="Maroon" title="c10">t</font></span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E2:36_1_1_1"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E1:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E5:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A13</font></span></a></span>;<br/><a NAME="E2:36_1_1_1_1_2_8"/><span class="kw">then </span><span class="lab"><font color="Green" title="E55">A38</font></span>: 
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_1_1"><span class="lab"><font color="Green" title="E23">A6</font></span></a>, <a class="txt" href="#E37:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A36</font></span></a>, <a class="txt" href="#E5:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/><span class="kw">assume </span><a NAME="E3:36_1_1_1_1_2_8"/>
<font color="Maroon">F<sub>1</sub></font>(<span class="p1">(<span class="default"><a href="memstr_0.html#K8" title="MEMSTR_0:func.8">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><span class="kw">hence </span><a NAME="E4:36_1_1_1_1_2_8"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1_1_1_1_2_8"><span class="lab"><font color="Green" title="E55">A38</font></span></a>, <a class="ref" href="int_1.html#T7" onmouseover="rs('int_1/T7')" onmouseout="rh()">INT_1:7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><span class="lab"><font color="Green" title="E55">A39</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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="funct_1.html#K1" title="FUNCT_1:func.1">.</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="c12">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#K10" title="COMPOS_1:func.10">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="c12">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#K10" title="COMPOS_1:func.10">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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E33:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E51">A34</font></span></a>, <a class="ref" href="scmpds_4.html#T8" onmouseover="rs('scmpds_4/T8')" onmouseout="rh()">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="c12">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#K10" title="COMPOS_1:func.10">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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E38">A21</font></span></a>, <a class="ref" href="extpro_1.html#T23" onmouseover="rs('extpro_1/T23')" onmouseout="rh()">EXTPRO_1:23</a></span>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a>, <a class="txt" href="#E3:36"><span class="lab"><font color="Green" title="E20">A3</font></span></a>, <a class="txt" href="#E2:36_1_1_1"><span class="lab"><font color="Green" title="E24">A7</font></span></a>, <a class="txt" href="#E1:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E21:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E40">A23</font></span></a></span>
;<br/><span class="lab"><font color="Green" title="E56">A40</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E30:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E49">A32</font></span></a>, <a class="ref" href="scmpds_2.html#T54" onmouseover="rs('scmpds_2/T54')" onmouseout="rh()">SCMPDS_2:54</a></span>
<br/>.= 
<font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>()
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E39:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E55">A39</font></span></a>, <a class="ref" href="extpro_1.html#T4" onmouseover="rs('extpro_1/T4')" onmouseout="rh()">EXTPRO_1:4</a></span>
;<br/><a NAME="E41:36_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A41</font></span>: 
 <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>),<font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="#E1:36_1_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E22:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="#E37:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A36</font></span></a>, <a class="txt" href="#E38:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E32:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A33</font></span></a></span>;<br/><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_1_1_1_1_2_11"><span class="kw">now </span> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds   <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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" title="b1">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c28">k</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="36_1_1_1_1_2_11_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_1_1_1_2_11_1"/>
( <font color="Maroon" title="c28">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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 or <font color="Maroon" title="c28">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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1_2_11_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_1_2_11_1_1"/>
<font color="Maroon" title="c28">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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="E2:36_1_1_1_1_2_11_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E58">A42</font></span>: 
<font color="Maroon" title="c28">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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="int_1.html#T7" onmouseover="rs('int_1/T7')" onmouseout="rh()">INT_1:7</a></span>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1_2_11_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_1_1_1_2_11_1_1_1"/>
( <font color="Maroon" title="c28">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="c12">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#K10" title="COMPOS_1:func.10">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="c28">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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1 )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:36_1_1_1_1_2_11_1_1"><span class="lab"><font color="Green" title="E58">A42</font></span></a>, <a class="ref" href="nat_1.html#T8" onmouseover="rs('nat_1/T8')" onmouseout="rh()">NAT_1:8</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1_2_11_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_1_2_11_1_1_1_1"/><span class="lab"><font color="Green" title="E59">A43</font></span>: 
<font color="Maroon" title="c28">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span></span>)</span>,<font color="Maroon" title="c10">t</font>)
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span>
<div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1_2_11_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:36_1_1_1_1_2_11_1_1_1_1_1_1"/>
( <font color="Maroon" title="c28">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  or <font color="Maroon" title="c28">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1_2_11_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_1_2_11_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c28">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c28">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="E2:36_1_1_1_1_2_11_1_1_1_1_1_1_1"/>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c28">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="#E2:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E6:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E31">A14</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="36_1_1_1_1_2_11_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c28">k</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c28">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c29">kn</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E60">A44</font></span>: 
<font color="Maroon" title="c28">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c29">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" onmouseover="rs('nat_1/T6')" onmouseout="rh()">NAT_1:6</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c30">kn</font> = <font color="Maroon" title="c29">kn</font> as   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> ;<br/><span class="kw">reconsider </span><font color="Maroon" title="c31">lm</font> =  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">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="c30">kn</font>)</span>)</span> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ;<br/><a NAME="E6:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c30">kn</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c28">k</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_1_1_2_11_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E60">A44</font></span></a>, <a class="ref" href="xreal_1.html#T29" onmouseover="rs('xreal_1/T29')" onmouseout="rh()">XREAL_1:29</a></span>;<br/><a NAME="E7:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c30">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="c12">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#K10" title="COMPOS_1:func.10">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="#E1:36_1_1_1_1_2_11_1_1_1_1"><span class="lab"><font color="Green" title="E59">A43</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/><a NAME="E8:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="memstr_0.html#K5" title="MEMSTR_0:func.5">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="c12">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#K10" title="COMPOS_1:func.10">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="c30">kn</font>)</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p5">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c30">kn</font>)</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E20:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E24:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E25:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="txt" href="#E16:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E13:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="ref" href="scmpds_7.html#T16" onmouseover="rs('scmpds_7/T16')" onmouseout="rh()">SCMPDS_7:16</a></span>;<br/><a NAME="E9:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A45</font></span>: 
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c28">k</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c31">lm</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_1_1_2_11_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E60">A44</font></span></a>, <a class="ref" href="extpro_1.html#T4" onmouseover="rs('extpro_1/T4')" onmouseout="rh()">EXTPRO_1:4</a></span>;<br/><a NAME="E10:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">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="c30">kn</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E42">A25</font></span></a>, <a class="txt" href="#E5:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="scmpds_6.html#D2" onmouseover="rs('scmpds_6/D2')" onmouseout="rh()">SCMPDS_6:def 2</a></span>;<br/><a NAME="E11:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c31">lm</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">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" onmouseover="rs('afinsq_1/T66')" onmouseout="rh()">AFINSQ_1:66</a></span>;<br/><a NAME="E12:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c31">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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <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="compos_1.html#T55" onmouseover="rs('compos_1/T55')" onmouseout="rh()">COMPOS_1:55</a></span>;<br/><a NAME="E13:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A46</font></span>: 
<font color="Maroon" title="c31">lm</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <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="int_1.html#T7" onmouseover="rs('int_1/T7')" onmouseout="rh()">INT_1:7</a></span>;<br/><a NAME="E14:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" onmouseover="rs('xreal_1/T6')" onmouseout="rh()">XREAL_1:6</a></span>;<br/><a NAME="E15:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c31">lm</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</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#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 3
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:36_1_1_1_1_2_11_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E62">A46</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/><a NAME="E16:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c31">lm</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#E23"><span class="lab"><font color="Green" title="E12">Lm3</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E17:36_1_1_1_1_2_11_1_1_1_1_1_1_2"/>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c28">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="#E9:36_1_1_1_1_2_11_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E61">A45</font></span></a>, <a class="ref" href="afinsq_1.html#T66" onmouseover="rs('afinsq_1/T66')" onmouseout="rh()">AFINSQ_1:66</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><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="36_1_1_1_1_2_11_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_1_2_11_1_1_1_2"/><span class="lab"><font color="Green" title="E59">A47</font></span>: 
<font color="Maroon" title="c28">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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="E2:36_1_1_1_1_2_11_1_1_1_2"/>
<span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Maroon">F<sub>4</sub></font>()</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="#E8:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E32">A15</font></span></a>, <a class="ref" href="compos_1.html#T62" onmouseover="rs('compos_1/T62')" onmouseout="rh()">COMPOS_1:62</a></span>;<br/><span class="kw">hence </span><a NAME="E3:36_1_1_1_1_2_11_1_1_1_2"/>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c28">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="#E4:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E20:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E39">A22</font></span></a>, <a class="txt" href="#E24:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E43">A26</font></span></a>, <a class="txt" href="#E25:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E44">A27</font></span></a>, <a class="txt" href="#E16:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E37">A20</font></span></a>, <a class="txt" href="#E13:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E35">A18</font></span></a>, <a class="txt" href="#E28:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E47">A30</font></span></a>, <a class="txt" href="#E1:36_1_1_1_1_2_11_1_1_1_2"><span class="lab"><font color="Green" title="E59">A47</font></span></a>, <a class="ref" href="scmpds_7.html#T18" onmouseover="rs('scmpds_7/T18')" onmouseout="rh()">SCMPDS_7:18</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><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="36_1_1_1_1_2_11_1_2"><span class="kw">suppose </span></a><a NAME="E1:36_1_1_1_1_2_11_1_2"/>
<font color="Maroon" title="c28">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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c29">nn</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><span class="kw"> such that </span><br/><a NAME="E3:36_1_1_1_1_2_11_1_2"/><span class="lab"><font color="Green" title="E58">A48</font></span>: 
<font color="Maroon" title="c28">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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c29">nn</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T10" onmouseover="rs('nat_1/T10')" onmouseout="rh()">NAT_1:10</a></span>;<br/><a NAME="E4:36_1_1_1_1_2_11_1_2"/>
 <a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c28">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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span>,<font color="Maroon" title="c29">nn</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:36_1_1_1_1_2_11_1_2"><span class="lab"><font color="Green" title="E58">A48</font></span></a>, <a class="ref" href="extpro_1.html#T4" onmouseover="rs('extpro_1/T4')" onmouseout="rh()">EXTPRO_1:4</a></span>;<br/><span class="kw">hence </span><a NAME="E5:36_1_1_1_1_2_11_1_2"/>
 <a href="memstr_0.html#K5" title="MEMSTR_0:func.5">IC</a> <span class="p1">(<span class="default"><a href="extpro_1.html#K5" title="EXTPRO_1:func.5">Comput</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p4">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c28">k</font>)</span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="compos_1.html#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="#E41:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E57">A41</font></span></a>, <a class="txt" href="#E32:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A33</font></span></a>, <a class="ref" href="scmpds_6.html#D2" onmouseover="rs('scmpds_6/D2')" onmouseout="rh()">SCMPDS_6:def 2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> 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="E43:36_1_1_1_1_2"/>
 <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="scmpds_6.html#D2" onmouseover="rs('scmpds_6/D2')" onmouseout="rh()">SCMPDS_6:def 2</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">Q</font></span><br/><a NAME="E44:36_1_1_1_1_2"/><span class="lab"><font color="Green" title="E58">A49</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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> <font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="E45:36_1_1_1_1_2"/>
 <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>),<font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="#E1:36_1_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a>, <a class="txt" href="#E22:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E41">A24</font></span></a>, <a class="txt" href="#E40:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E56">A40</font></span></a>, <a class="txt" href="#E37:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E53">A36</font></span></a>, <a class="txt" href="#E38:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E54">A37</font></span></a>, <a class="txt" href="#E32:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A33</font></span></a></span>;<br/><a NAME="E46:36_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p3">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">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#K10" title="COMPOS_1:func.10">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#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E50">A33</font></span></a>, <a class="txt" href="#E44:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E58">A49</font></span></a>, <a class="ref" href="scmpds_6.html#D3" onmouseover="rs('scmpds_6/D3')" onmouseout="rh()">SCMPDS_6:def 3</a></span>;<br/><a NAME="E47:36_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">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#K10" title="COMPOS_1:func.10">stop</a> <span class="p2">(<span class="default"><a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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" onmouseover="rs('extpro_1/T22')" onmouseout="rh()">EXTPRO_1:22</a></span>;<br/><span class="kw">hence </span><a NAME="E48:36_1_1_1_1_2"/>
 <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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="c12">Q</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:36_1_1_1_1_2"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="ref" href="scmpds_6.html#D3" onmouseover="rs('scmpds_6/D3')" onmouseout="rh()">SCMPDS_6:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><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="E3:36_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c9">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1]
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</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="E2:36_1"/><span class="lab"><font color="Green" title="E22">A50</font></span>: 
<font color="Maroon">S<sub>1</sub></font>[ <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> ]
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="36_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#K5" title="NUMBERS:func.5">0</a>  <a href="memstr_0.html#V5" title="MEMSTR_0:attr.5">-started</a>  <a href="memstr_0.html#NM2" title="MEMSTR_0:NM.2">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">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#K5" title="NUMBERS:func.5">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="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() holds <br/>(  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K2" title="SCMPDS_8:func.2">while&gt;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" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon">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#K5" title="NUMBERS:func.5">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="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>() implies (  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K2" title="SCMPDS_8:func.2">while&gt;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="E1:36_1_2"/><span class="lab"><font color="Green" title="E23">A51</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#K5" title="NUMBERS:func.5">0</a> 
 <span class="kw">and </span><br/><a NAME="E2:36_1_2"/><span class="lab"><font color="Green" title="E24">A52</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="E3:36_1_2"/><span class="lab"><font color="Green" title="E25">A53</font></span>: 
<font color="Maroon" title="c10">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon">F<sub>5</sub></font>()
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K2" title="SCMPDS_8:func.2">while&gt;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="E4:36_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#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36_1_2"><span class="lab"><font color="Green" title="E23">A51</font></span></a></span>;<br/>
<a NAME="E5:36_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c10">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">DataLoc</a> (<span class="p2">(<span class="default"><font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:36"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E2:36_1_2"><span class="lab"><font color="Green" title="E24">A52</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:36_1_2"/>
(  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K2" title="SCMPDS_8:func.2">while&gt;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="#E3:36_1_2"><span class="lab"><font color="Green" title="E25">A53</font></span></a>, <a class="ref" href="scmpds_8.html#T20" target="_self" onmouseover="rs('scmpds_8/T20')" onmouseout="rh()">Th18</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E3:36_1"/>
 for <font color="Olive" title="b1">k</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">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#S2" onmouseover="rs('nat_1/S2')" onmouseout="rh()">NAT_1:sch 2</a>(<a class="txt" href="#E2:36_1"><span class="lab"><font color="Green" title="E22">A50</font></span></a>, <a class="txt" href="#E1:36_1"><span class="lab"><font color="Green" title="E21">A4</font></span></a>);<br/></span>
<a NAME="E4:36_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="E5:36_1"/>
(  <a href="scmpds_8.html#K2" title="SCMPDS_8:func.2">while&gt;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#K2" title="SCMPDS_8:func.2">while&gt;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="#E2:36"><span class="lab"><font color="Green" title="E19">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
