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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="scmfsa_2.html#M1">Int-Location</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:19_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 or <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0 )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_1"><b>suppose </b></a><a NAME="E1:19_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:19_1_1"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>and </b><br/><a NAME="E4:19_1_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="scmfsa_7.html#K2" target="_self">:=</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_7.html#K1" target="_self">Load</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmfsa_2.html#K8">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finsop_1.html#K1">|-&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K9">AddTo</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#D2" target="_self">Def2</a></i>;<br/><b>thus </b><a NAME="E5:19_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="scmfsa_7.html#K2" target="_self">:=</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_7.html#K1" target="_self">Load</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" target="_self">aSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E3:19_1_1"><i><font color="Green">E18</font></i></a>, <a class="txt" href="scmfsa_7.html#E4:19_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="scmfsa_7.html#D3" target="_self">Def3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="19_1_2"><b>suppose </b></a><a NAME="E1:19_1_2"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 0
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:19_1_2"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 1
 <b>and </b><br/><a NAME="E4:19_1_2"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="scmfsa_7.html#K2" target="_self">:=</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_7.html#K1" target="_self">Load</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="scmfsa_2.html#K8">:=</a> <span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="finseq_1.html#K8">^</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finsop_1.html#K1">|-&gt;</a> <span class="p4">(<span class="default"><a href="scmfsa_2.html#K10">SubFrom</a> <font color="Maroon">c<sub>1</sub></font>,<span class="p5">(<span class="default"><a href="scmfsa_2.html#K4">intloc</a> 0</span>)</span></span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="ref" href="scmfsa_7.html#D2" target="_self">Def2</a></i>;<br/><b>thus </b><a NAME="E5:19_1_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="scmfsa_7.html#K2" target="_self">:=</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmfsa_7.html#K1" target="_self">Load</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scmfsa_7.html#K3" target="_self">aSeq</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><span class="p3">(<span class="default"><a href="ami_1.html#K5">halt</a> <a href="scmfsa_2.html#K1">SCM+FSA</a> </span>)</span></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span>
 <b>by </b><i><a class="txt" href="scmfsa_7.html#E1:19_1_2"><i><font color="Green">E18</font></i></a>, <a class="txt" href="scmfsa_7.html#E3:19_1_2"><i><font color="Green">E19</font></i></a>, <a class="txt" href="scmfsa_7.html#E4:19_1_2"><i><font color="Green">E20</font></i></a>, <a class="ref" href="scmfsa_7.html#D3" target="_self">Def3</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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