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<span class="kw">let </span><font color="Maroon" title="c11">term</font> be   <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">aux</font>, <font color="Olive" title="b2">n</font>, <font color="Olive" title="b3">k</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <br/> for <font color="Olive" title="b4">s</font> being   <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of <font color="Olive" title="b2">n</font>,<font color="Olive" title="b2">n</font>,<font color="Olive" title="b3">k</font>,<span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Olive" title="b1">aux</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>, <a href="pre_poly.html#K2" title="PRE_POLY:func.2">&lt;*&gt;</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b1">aux</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="scm_comp.html#K21" title="SCM_COMP:func.21">max_Data-Loc_in</a> <font color="Maroon" title="c11">term</font> holds <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b4">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Olive" title="b4">s</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b4">s</font></span>)</span>,<font color="Olive" title="b4">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Olive" title="b1">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Olive" title="b4">s</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b4">s</font></span>)</span>,<font color="Olive" title="b4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Olive" title="b1">aux</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c12">aux</font>, <font color="Maroon" title="c13">n</font>, <font color="Maroon" title="c14">k</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">s</font> being   <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of <font color="Maroon" title="c13">n</font>,<font color="Maroon" title="c13">n</font>,<font color="Maroon" title="c14">k</font>,<span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>, <a href="pre_poly.html#K2" title="PRE_POLY:func.2">&lt;*&gt;</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Maroon" title="c12">aux</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="scm_comp.html#K21" title="SCM_COMP:func.21">max_Data-Loc_in</a> <font color="Maroon" title="c11">term</font> holds <br/>(  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Olive" title="b1">s</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Maroon" title="c12">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Olive" title="b1">s</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Olive" title="b1">s</font></span>)</span>,<font color="Olive" title="b1">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c15">s</font> be    <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of <font color="Maroon" title="c13">n</font>,<font color="Maroon" title="c13">n</font>,<font color="Maroon" title="c14">k</font>,<span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span>, <a href="pre_poly.html#K2" title="PRE_POLY:func.2">&lt;*&gt;</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c12">aux</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="scm_comp.html#K21" title="SCM_COMP:func.21">max_Data-Loc_in</a> <font color="Maroon" title="c11">term</font> implies (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c15">s</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Maroon" title="c12">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c15">s</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span> ) )</span><br/>





<span class="kw">assume </span><a NAME="E1:37"/><span class="lab"><font color="Green" title="E27">A1</font></span>: 
<font color="Maroon" title="c12">aux</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="scm_comp.html#K21" title="SCM_COMP:func.21">max_Data-Loc_in</a> <font color="Maroon" title="c11">term</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c15">s</font> &amp; <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Maroon" title="c12">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c15">s</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span> )</span><br/>

<a NAME="E2:37"/>
<font color="Maroon" title="c15">s</font> is    <a href="scm_1.html#M1" title="SCM_1:mode.1">State-consisting</a> of <font color="Maroon" title="c13">n</font>,<font color="Maroon" title="c13">n</font>,<font color="Maroon" title="c14">k</font>, <a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font>, <a href="pre_poly.html#K2" title="PRE_POLY:func.2">&lt;*&gt;</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_comp.html#T1" target="_self" title="SCM_COMP:th.1">Th1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c16">i</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> , <font color="Maroon" title="c17">u</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> <span class="kw"> such that </span><br/><a NAME="E4:37"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c17">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c16">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:37"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
<font color="Maroon" title="c16">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E6:37"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10" title="AMI_1:func.10">Comput</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font>,<font color="Maroon" title="c16">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c16">i</font>
 <span class="kw">and </span><br/><a NAME="E7:37"/><span class="lab"><font color="Green" title="E31">A5</font></span>: 
 <a href="ami_1.html#K6" title="AMI_1:func.6">IC</a> <font color="Maroon" title="c17">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 <span class="kw">and </span><br/><a NAME="E8:37"/><span class="lab"><font color="Green" title="E32">A6</font></span>: 
<font color="Maroon" title="c17">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Maroon" title="c12">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c15">s</font>
 <span class="kw">and </span><br/><a NAME="E9:37"/>
for <font color="Olive" title="b1">dn</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b1">dn</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">aux</font> holds <br/><font color="Maroon" title="c15">s</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Olive" title="b1">dn</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c17">u</font> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Olive" title="b1">dn</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E27">A1</font></span></a>, <a class="ref" href="scm_comp.html#T14" target="_self" title="SCM_COMP:th.14">Th14</a></span>;<br/>
<a NAME="E10:37"/>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="afinsq_1.html#T38" title="AFINSQ_1:th.38">AFINSQ_1:38</a></span>;<br/>
<a NAME="E11:37"/><span class="kw">then </span>
 <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="afinsq_1.html#T20" title="AFINSQ_1:th.20">AFINSQ_1:20</a></span>;<br/>
<a NAME="E12:37"/><span class="kw">then </span>
<font color="Maroon" title="c16">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E33">A7</font></span>: <font color="Maroon" title="c15">s</font> <a href="ami_1.html#K12" title="AMI_1:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c13">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c16">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span> <a href="ordinal4.html#K1" title="ORDINAL4:func.1">^</a> <span class="p2"><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> </span>)</span></span><a href="afinsq_1.html#K5" title="AFINSQ_1:func.5">%&gt;</a></span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_1.html#D1" title="SCM_1:def.1">SCM_1:def 1</a></span>
<br/>.= 
 <a href="ami_1.html#K5" title="AMI_1:func.5">halt</a> <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="ref" href="afinsq_1.html#T40" title="AFINSQ_1:th.40">AFINSQ_1:40</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E14:37"/>
 <a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font> <a href="ami_1.html#R1" title="AMI_1:pred.1">halts_on</a> <font color="Maroon" title="c15">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="ref" href="scm_1.html#T3" title="SCM_1:th.3">SCM_1:3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Maroon" title="c12">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c15">s</font> &amp;  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E15:37"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K11" title="AMI_1:func.11">Result</a> <span class="p2">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font></span>)</span> <a href="ami_3.html#K2" title="AMI_3:func.2">.</a> <span class="p1">(<span class="default"><a href="ami_3.html#K11" title="AMI_3:func.11">dl.</a> <font color="Maroon" title="c12">aux</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">term</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c15">s</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="txt" href="#E8:37"><span class="lab"><font color="Green" title="E32">A6</font></span></a>, <a class="txt" href="#E13:37"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="ref" href="scm_1.html#T4" title="SCM_1:th.4">SCM_1:4</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span></span><br/>

<a NAME="E16:37"/>
<font color="Maroon" title="c13">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <font color="Maroon" title="c16">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c13">n</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">i</font> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>
 
;<br/>
<span class="kw">hence </span><a NAME="E17:37"/>
 <a href="ami_1.html#K23" title="AMI_1:func.23">LifeSpan</a> <span class="p1">(<span class="default"><a href="ami_1.html#K8" title="AMI_1:func.8">ProgramPart</a> <font color="Maroon" title="c15">s</font></span>)</span>,<font color="Maroon" title="c15">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="afinsq_1.html#K1" title="AFINSQ_1:func.1">len</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K19" title="SCM_COMP:func.19">SCM-Compile</a> <font color="Maroon" title="c11">term</font>,<font color="Maroon" title="c12">aux</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:37"><span class="lab"><font color="Green" title="E28">A2</font></span></a>, <a class="txt" href="#E5:37"><span class="lab"><font color="Green" title="E29">A3</font></span></a>, <a class="txt" href="#E6:37"><span class="lab"><font color="Green" title="E30">A4</font></span></a>, <a class="txt" href="#E7:37"><span class="lab"><font color="Green" title="E31">A5</font></span></a>, <a class="txt" href="#E13:37"><span class="lab"><font color="Green" title="E33">A7</font></span></a>, <a class="ref" href="scm_1.html#T17" title="SCM_1:th.17">SCM_1:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
