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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ami_1.html#NM3">Instruction</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>assume </b><a NAME="E1:81"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#R1" target="_self">valid_at</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<div><i><font color="Green">E53</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="81_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:81_1"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 0
 ;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:81_1"/><i><font color="Green">E54</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K4">goto</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:81"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self">Def11</a></i>;<br/><b>take </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/><b>thus </b><a NAME="E4:81_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="scmpds_2.html#K4">goto</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:81_1"><i><font color="Green">E54</font></i></a></i>;<br/><b>thus </b><a NAME="E5:81_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:81"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmpds_4.html#E3:81_1"><i><font color="Green">E54</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E54</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="81_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:81_2"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 4
 ;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:81_2"/><i><font color="Green">E55</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="scmpds_2.html#K8">&lt;&gt;0_goto</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:81"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self">Def11</a></i>;<br/><b>take </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font>;<br/><b>thus </b><a NAME="E4:81_2"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="scmpds_2.html#K8">&lt;&gt;0_goto</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:81_2"><i><font color="Green">E55</font></i></a></i>;<br/><b>thus </b><a NAME="E5:81_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:81"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmpds_4.html#E3:81_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E55</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="81_3"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:81_3"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 5
 ;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:81_3"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:81"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self">Def11</a></i>;<br/><b>take </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font>;<br/><b>thus </b><a NAME="E4:81_3"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="scmpds_2.html#K9">&lt;=0_goto</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:81_3"><i><font color="Green">E56</font></i></a></i>;<br/><b>thus </b><a NAME="E5:81_3"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:81"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmpds_4.html#E3:81_3"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="81_4"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:81_4"/>
 <a href="ami_5.html#K1">InsCode</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 6
 ;<br/><b>then consider </b><font color="Maroon">c<sub>4</sub></font> being    <a href="scmpds_2.html#M1">Int_position</a> , <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> being   <a href="int_1.html#NM1">Integer</a><b> such that </b><br/><a NAME="E3:81_4"/><i><font color="Green">E56</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="scmpds_2.html#K10">&gt;=0_goto</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0 )
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:81"><i><font color="Green">E52</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self">Def11</a></i>;<br/><b>take </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>5</sub></font>;<br/><b>take </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font>;<br/><b>thus </b><a NAME="E4:81_4"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="scmpds_2.html#K10">&gt;=0_goto</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E3:81_4"><i><font color="Green">E56</font></i></a></i>;<br/><b>thus </b><a NAME="E5:81_4"/>
<font color="Maroon">c<sub>3</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 <b>by </b><i><a class="txt" href="scmpds_4.html#E1:81"><i><font color="Green">E52</font></i></a>, <a class="txt" href="scmpds_4.html#E3:81_4"><i><font color="Green">E56</font></i></a>, <a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:81"/>
<font color="Maroon">c<sub>1</sub></font> <a href="scmpds_4.html#R1" target="_self">valid_at</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scmpds_4.html#E2:81"><i><font color="Green">E53</font></i></a>, <a class="txt" href="scmpds_4.html#E3:81"><i><font color="Green">E54</font></i></a>, <a class="txt" href="scmpds_4.html#E4:81"><i><font color="Green">E55</font></i></a>, <a class="ref" href="scmpds_4.html#D11" target="_self">Def11</a></i>;<br/>


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