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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/>



<b>assume </b><a NAME="E1:3"/>
 <a href="scmpds_3.html#K2">inspos</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then </b><i><font color="Green">E4</font></i>: <font color="Maroon">c<sub>2</sub></font> = 
 <a href="ami_3.html#K16">il.</a> <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="scmpds_3.html#D2">SCMPDS_3:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#D20">AMI_3:def 20</a></i>
<br/>.= 
2 <a href="nat_1.html#K2">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>

;<br/>
<a NAME="E3:3"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="int_2.html#K1">abs</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4 = 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K3">div</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="txt" href="scmp_gcd.html#E2:3"><i><font color="Green">E4</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default">2 <a href="nat_1.html#K2">*</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 4
<b>by </b><i><a class="ref" href="nat_1.html#T72">NAT_1:72</a></i>
<br/>.= 
<span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 2

<br/>.= 
 <a href="ami_3.html#K16">il.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="ami_3.html#D20">AMI_3:def 20</a></i>
<br/>.= 
 <a href="scmpds_3.html#K2">inspos</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span>
<b>by </b><i><a class="ref" href="scmpds_3.html#D2">SCMPDS_3:def 2</a></i>
;<br/><br/>


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