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<b>let </b><font color="Maroon" title="c1">a</font> be    <a href="scmpds_2.html#M1" title="SCMPDS_2:mode.1">Int_position</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">l</font> being   <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <br/> for <font color="Olive" title="b2">k1</font>, <font color="Olive" title="b3">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds   <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Olive" title="b2">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Olive" title="b3">k2</font></span>)</span>,<font color="Olive" title="b1">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Olive" title="b1">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Olive" title="b1">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><b>let </b><font color="Maroon" title="c2">l</font> be    <a href="ami_1.html#M3" title="AMI_1:mode.3">Instruction-Location</a> of  <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">k1</font>, <font color="Olive" title="b2">k2</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a> holds   <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Olive" title="b1">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Olive" title="b2">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Olive" title="b2">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><b>let </b><font color="Maroon" title="c3">k1</font>, <font color="Maroon" title="c4">k2</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/>







<b>set </b><font color="Maroon" title="c5">i</font> = <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font>;<br/>
<b>set </b><font color="Maroon" title="c6">t</font> =  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c7">w1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> ;<br/>
<a NAME="E2:21"/><i><font color="Green" title="E17">A1</font></i>: 
 <a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font>
 
<b>by </b><i><a class="ref" href="scmpds_9.html#T3" target="_self" title="SCMPDS_9:th.3">Th8</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font></span>
<div class="add"><b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font> implies <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )</span><br/><b>assume </b><a NAME="E1:21_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><b>then consider </b><font color="Maroon" title="c9">s</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> <b> such that </b><br/><a NAME="E3:21_1"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <font color="Maroon" title="c9">s</font></span>)</span>
 <b>and </b><br/><a NAME="E4:21_1"/><i><font color="Green" title="E19">A3</font></i>: 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c9">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">l</font>
 <b>and </b><br/><a NAME="E5:21_1"/><i><font color="Green" title="E20">A4</font></i>: 
<font color="Maroon" title="c9">s</font> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font>
 ;<br/><b>consider </b><font color="Maroon" title="c10">m1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <b> such that </b><br/><a NAME="E7:21_1"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c10">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <font color="Maroon" title="c9">s</font>
 <b>and </b><br/><a NAME="E8:21_1"/><i><font color="Green" title="E22">A6</font></i>: 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <font color="Maroon" title="c9">s</font>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20" title="SCMPDS_2:def.20">SCMPDS_2:def 20</a></i>;<br/><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_1_1"/>
( <font color="Maroon" title="c9">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or <font color="Maroon" title="c9">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1_1"><b>suppose </b></a><a NAME="E1:21_1_1_1"/><i><font color="Green" title="E23">A7</font></i>: 
<font color="Maroon" title="c9">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><div class="add"><font color="Maroon" title="c8">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c9">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E3:21_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="scmpds_9.html#E4:21_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E5:21_1"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="ami_1.html#T131" title="AMI_1:th.131">AMI_1:131</a></i>
<br/>.= 
 <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E2:21"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="scmpds_9.html#E4:21_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E7:21_1"><i><font color="Green" title="E21">A5</font></i></a>, <a class="txt" href="scmpds_9.html#E8:21_1"><i><font color="Green" title="E22">A6</font></i></a>, <a class="txt" href="scmpds_9.html#E1:21_1_1_1"><i><font color="Green" title="E23">A7</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
;<br/><b>hence </b><a NAME="E3:21_1_1_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_1_1_2"><b>suppose </b></a><a NAME="E1:21_1_1_2"/><i><font color="Green" title="E23">A8</font></i>: 
<font color="Maroon" title="c9">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span></span><br/><div class="add"><font color="Maroon" title="c8">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c9">s</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E3:21_1"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="scmpds_9.html#E4:21_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E5:21_1"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="ami_1.html#T131" title="AMI_1:th.131">AMI_1:131</a></i>
<br/>.= 
 <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font>
<b>by </b><i><a class="txt" href="scmpds_9.html#E4:21_1"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="scmpds_9.html#E1:21_1_1_2"><i><font color="Green" title="E23">A8</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
;<br/><b>hence </b><a NAME="E3:21_1_1_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c8">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font> )</span><br/>

<b>assume </b><a NAME="E4:21"/><i><font color="Green" title="E18">A9</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><span class="p2">(<span class="default"><a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font></span>)</span>,<span class="p2">(<span class="default"><a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p4">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span></span>)</span></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font></span><br/>

<b>consider </b><font color="Maroon" title="c9">s</font> being   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> ;<br/>
<a NAME="E6:21"/>
<font color="Maroon" title="c2">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> 
 
<b>by </b><i><a class="ref" href="ami_1.html#D4" title="AMI_1:def.4">AMI_1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c10">il1</font> = <font color="Maroon" title="c2">l</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span> <b>by </b><i><a class="ref" href="ami_1.html#D11" title="AMI_1:def.11">AMI_1:def 11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c11">I</font> = <font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <font color="Maroon" title="c2">l</font> <b>by </b><i><a class="ref" href="ami_1.html#D14" title="AMI_1:def.14">AMI_1:def 14</a></i>;<br/>
<b>set </b><font color="Maroon" title="c12">u</font> = <font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_2"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_2"/>
( <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font> or <font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span> )
 </span><b>by </b><i><a class="txt" href="scmpds_9.html#E4:21"><i><font color="Green" title="E18">A9</font></i></a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_2_1"><b>suppose </b></a><a NAME="E1:21_2_1"/><i><font color="Green" title="E19">A10</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmnorm.html#K1" title="SCMNORM:func.1">Next</a> <font color="Maroon" title="c2">l</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c13">u1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span>;<br/><b>set </b><font color="Maroon" title="c14">u2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span>;<br/><a NAME="E2:21_2_1"/><i><font color="Green" title="E20">A11</font></i>: 
<font color="Maroon" title="c2">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53" title="SCMPDS_2:th.53">SCMPDS_2:53</a></i>;<br/><a NAME="E3:21_2_1"/>
<font color="Maroon" title="c2">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53" title="SCMPDS_2:th.53">SCMPDS_2:53</a></i>;<br/><b>then </b><i><font color="Green" title="E21">A12</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c2">l</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c2">l</font>
<b>by </b><i><a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c2">l</font>
<b>by </b><i><a class="txt" href="scmpds_9.html#E2:21_2_1"><i><font color="Green" title="E20">A11</font></i></a>, <a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font>
<b>by </b><i><a class="ref" href="ami_1.html#T129" title="AMI_1:th.129">AMI_1:129</a></i>
;<br/><i><font color="Green" title="E22">A13</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15" title="AMI_1:def.15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a>, <a class="ref" href="scmpds_2.html#T52" title="SCMPDS_2:th.52">SCMPDS_2:52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a>, <a class="ref" href="scmpds_2.html#T52" title="SCMPDS_2:th.52">SCMPDS_2:52</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15" title="AMI_1:def.15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon" title="c10">il1</font>
<b>by </b><i><a class="ref" href="ami_1.html#T129" title="AMI_1:th.129">AMI_1:129</a></i>
;<br/><a NAME="E6:21_2_1"/><i><font color="Green" title="E23">A14</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 <b>by </b><i><a class="ref" href="funct_7.html#T96" title="FUNCT_7:th.96">FUNCT_7:96</a></i>;<br/><a NAME="E7:21_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2_1_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_2_1_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_2_1_3_1"/>
( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font> or <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_2_1_3_1_1"><b>suppose </b></a><a NAME="E1:21_2_1_3_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><div class="add"><b>hence </b><a NAME="E2:21_2_1_3_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="scmpds_9.html#E6:21_2_1"><i><font color="Green" title="E23">A14</font></i></a>, <a class="ref" href="funct_7.html#T96" title="FUNCT_7:th.96">FUNCT_7:96</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_2_1_3_1_2"><b>suppose </b></a><a NAME="E1:21_2_1_3_1_2"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><div class="add"><a NAME="E2:21_2_1_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a></i>;<br/><b>hence </b><a NAME="E3:21_2_1_3_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="funct_7.html#T96" title="FUNCT_7:th.96">FUNCT_7:96</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>then </b><font color="Maroon" title="c8">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E1:21_2_1"><i><font color="Green" title="E19">A10</font></i></a>, <a class="txt" href="scmpds_9.html#E5:21_2_1"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> 1</span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E4:21_2_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="txt" href="scmpds_9.html#E5:21_2_1"><i><font color="Green" title="E22">A13</font></i></a>, <a class="ref" href="ami_1.html#T131" title="AMI_1:th.131">AMI_1:131</a></i>
;<br/><b>hence </b><a NAME="E9:21_2_1"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font>
 <b>by </b><i><a class="txt" href="scmpds_9.html#E4:21_2_1"><i><font color="Green" title="E21">A12</font></i></a>, <a class="txt" href="scmpds_9.html#E5:21_2_1"><i><font color="Green" title="E22">A13</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_2_2"><b>suppose </b></a><a NAME="E1:21_2_2"/><i><font color="Green" title="E19">A15</font></i>: 
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">k2</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><a href="scmpds_9.html#K3" title="SCMPDS_9:func.3">locnum</a> <font color="Maroon" title="c2">l</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font></span><br/><div class="add"><b>set </b><font color="Maroon" title="c13">u1</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>;<br/><b>set </b><font color="Maroon" title="c14">u2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span>;<br/><a NAME="E2:21_2_2"/><i><font color="Green" title="E20">A16</font></i>: 
<font color="Maroon" title="c2">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53" title="SCMPDS_2:th.53">SCMPDS_2:53</a></i>;<br/><a NAME="E3:21_2_2"/>
<font color="Maroon" title="c2">l</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font>
 <b>by </b><i><a class="ref" href="scmpds_2.html#T53" title="SCMPDS_2:th.53">SCMPDS_2:53</a></i>;<br/><b>then </b><i><font color="Green" title="E21">A17</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c2">l</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c2">l</font>
<b>by </b><i><a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K13" title="AMI_1:func.13">.</a> <font color="Maroon" title="c2">l</font>
<b>by </b><i><a class="txt" href="scmpds_9.html#E2:21_2_2"><i><font color="Green" title="E20">A16</font></i></a>, <a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a></i>
<br/>.= 
<font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font>
<b>by </b><i><a class="ref" href="ami_1.html#T129" title="AMI_1:th.129">AMI_1:129</a></i>
;<br/><i><font color="Green" title="E22">A18</font></i>:  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15" title="AMI_1:def.15">AMI_1:def 15</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a>, <a class="ref" href="scmpds_2.html#T52" title="SCMPDS_2:th.52">SCMPDS_2:52</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a>, <a class="ref" href="scmpds_2.html#T52" title="SCMPDS_2:th.52">SCMPDS_2:52</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="ami_1.html#D15" title="AMI_1:def.15">AMI_1:def 15</a></i>
<br/>.= 
<font color="Maroon" title="c10">il1</font>
<b>by </b><i><a class="ref" href="ami_1.html#T129" title="AMI_1:th.129">AMI_1:129</a></i>
;<br/><a NAME="E6:21_2_2"/><i><font color="Green" title="E23">A19</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="funct_7.html#T96" title="FUNCT_7:th.96">FUNCT_7:96</a></i>;<br/><a NAME="E7:21_2_2"/><i><font color="Green" title="E24">A20</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2_2_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_2_2_3_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:21_2_2_3_1"/>
( <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font> or <font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_2_2_3_1_1"><b>suppose </b></a><a NAME="E1:21_2_2_3_1_1"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><div class="add"><b>hence </b><a NAME="E2:21_2_2_3_1_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="txt" href="scmpds_9.html#E6:21_2_2"><i><font color="Green" title="E23">A19</font></i></a>, <a class="ref" href="funct_7.html#T96" title="FUNCT_7:th.96">FUNCT_7:96</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="21_2_2_3_1_2"><b>suppose </b></a><a NAME="E1:21_2_2_3_1_2"/>
<font color="Maroon" title="c1">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><br/><div class="add"><a NAME="E2:21_2_2_3_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T88" title="FUNCT_4:th.88">FUNCT_4:88</a></i>;<br/><b>hence </b><a NAME="E3:21_2_2_3_1_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 <b>by </b><i><a class="ref" href="funct_7.html#T96" title="FUNCT_7:th.96">FUNCT_7:96</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

</div><b>end;</b></div><b>consider </b><font color="Maroon" title="c15">m1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a> <b> such that </b><br/><a NAME="E9:21_2_2"/><i><font color="Green" title="E25">A21</font></i>: 
<font color="Maroon" title="c15">m1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E10:21_2_2"/><i><font color="Green" title="E26">A22</font></i>: 
 <a href="scmpds_2.html#K18" title="SCMPDS_2:func.18">ICplusConst</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p0">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span>,<font color="Maroon" title="c4">k2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="int_2.html#K1" title="INT_2:func.1">abs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">m1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">k2</font></span>)</span>
 <b>by </b><i><a class="ref" href="scmpds_2.html#D20" title="SCMPDS_2:def.20">SCMPDS_2:def 20</a></i>;<br/><font color="Maroon" title="c8">x</font> = 
<span class="p1">(<span class="default"><a href="ami_1.html#K4" title="AMI_1:func.4">Exec</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E2:21"><i><font color="Green" title="E17">A1</font></i></a>, <a class="txt" href="scmpds_9.html#E1:21_2_2"><i><font color="Green" title="E19">A15</font></i></a>, <a class="txt" href="scmpds_9.html#E5:21_2_2"><i><font color="Green" title="E22">A18</font></i></a>, <a class="txt" href="scmpds_9.html#E7:21_2_2"><i><font color="Green" title="E24">A20</font></i></a>, <a class="txt" href="scmpds_9.html#E9:21_2_2"><i><font color="Green" title="E25">A21</font></i></a>, <a class="txt" href="scmpds_9.html#E10:21_2_2"><i><font color="Green" title="E26">A22</font></i></a>, <a class="ref" href="scmpds_2.html#T68" title="SCMPDS_2:th.68">SCMPDS_2:68</a></i>
<br/>.= 
 <a href="ami_1.html#K7" title="AMI_1:func.7">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K9" title="AMI_1:func.9">Following</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="scmpds_2.html#K3" title="SCMPDS_2:func.3">DataLoc</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon" title="c9">s</font> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <a href="scmpds_2.html#K1" title="SCMPDS_2:func.1">SCMPDS</a> </span>)</span>,<font color="Maroon" title="c2">l</font> <a href="ami_1.html#K17" title="AMI_1:func.17">--&gt;</a> <font color="Maroon" title="c10">il1</font>,<font color="Maroon" title="c11">I</font></span>)</span></span>)</span> <a href="ami_1.html#K36" title="AMI_1:func.36">+*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span> <a href="scmpds_2.html#K2" title="SCMPDS_2:func.2">.</a> <font color="Maroon" title="c1">a</font></span>)</span>,<font color="Maroon" title="c3">k1</font></span>)</span> <a href="scmpds_3.html#K1" title="SCMPDS_3:func.1">.--&gt;</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="scmpds_9.html#E4:21_2_2"><i><font color="Green" title="E21">A17</font></i></a>, <a class="txt" href="scmpds_9.html#E5:21_2_2"><i><font color="Green" title="E22">A18</font></i></a>, <a class="ref" href="ami_1.html#T131" title="AMI_1:th.131">AMI_1:131</a></i>
;<br/><b>hence </b><a NAME="E12:21_2_2"/>
<font color="Maroon" title="c8">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="amistd_1.html#K1" title="AMISTD_1:func.1">NIC</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">a</font>,<font color="Maroon" title="c3">k1</font> <a href="scmpds_2.html#K9" title="SCMPDS_2:func.9">&lt;=0_goto</a> <font color="Maroon" title="c4">k2</font></span>)</span>,<font color="Maroon" title="c2">l</font>
 <b>by </b><i><a class="txt" href="scmpds_9.html#E4:21_2_2"><i><font color="Green" title="E21">A17</font></i></a>, <a class="txt" href="scmpds_9.html#E5:21_2_2"><i><font color="Green" title="E22">A18</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div>

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