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<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="scmpds_4.html#V3">shiftable</a> <a href="scmpds_5.html#V3">No-StopCode</a> <a href="scmpds_4.html#NM1">Program-block</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="scmpds_2.html#M1">Int_position</a> ;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="int_1.html#NM1">Integer</a>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>









<b>set </b><font color="Maroon">c<sub>11</sub></font> =  <a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/>
<b>assume </b><a NAME="E1:18"/><i><font color="Green">E18</font></i>: 
 <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<b>assume </b><a NAME="E2:18"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 ;<br/>

<b>assume </b><a NAME="E3:18"/><i><font color="Green">E20</font></i>: 
1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E4:18"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> )
 ;<br/>

<b>assume </b><a NAME="E5:18"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> <br/>for <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>9</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> <font color="Olive">b<sub>4</sub></font></span>)</span></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>5</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; ( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>6</sub></font> &amp; <font color="Olive">b<sub>7</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font> ) or <font color="Olive">b<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>7</sub></font> ) holds <br/>( <font color="Maroon">c<sub>4</sub></font> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Olive">b<sub>1</sub></font> &amp; <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( for <font color="Olive">b<sub>8</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>8</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> ) &amp; ( <font color="Olive">b<sub>6</sub></font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>7</sub></font> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 &amp; ( for <font color="Olive">b<sub>8</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>8</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> ) ) ) &amp; ( <font color="Olive">b<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>7</sub></font> implies ( <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2">*</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 3 &amp; ( for <font color="Olive">b<sub>8</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st ( ( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>8</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>6</sub></font> ) or ( <font color="Olive">b<sub>7</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>8</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>9</sub></font> ) ) holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> ) &amp; ex <font color="Olive">b<sub>8</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <br/>( <font color="Olive">b<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>8</sub></font> &amp; <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>7</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Olive">b<sub>5</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span> <a href="xcmplx_0.html#K6">-</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 2</span>)</span></span>)</span> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Olive">b<sub>5</sub></font> <a href="nat_1.html#K1">+</a> 3</span>)</span></span>)</span> &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>8</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>9</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> ) &amp; ( for <font color="Olive">b<sub>9</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>8</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">b<sub>9</sub></font> &amp; <font color="Olive">b<sub>9</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>7</sub></font> holds <br/><span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>9</sub></font></span>)</span></span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <span class="p1">(<span class="default"><a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Olive">b<sub>8</sub></font></span>)</span></span>)</span> ) ) ) ) &amp; ( <font color="Olive">b<sub>2</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a> <font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="scpisort.html#R1">is_FinSequence_on</a>  <a href="scmpds_4.html#K9">IExec</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>8</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> implies <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="rfinseq.html#R1">are_fiberwise_equipotent</a>  ) )
 ;<br/>

<div><i><font color="Green">E23</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="18_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>12</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="scmpds_2.html#K1">SCMPDS</a> ;<br/><b>assume </b><a NAME="E1:18_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <a href="ami_2.html#K2">SCM-Data-Loc</a> 
 ;<br/><a NAME="E2:18_1"/><b>then </b><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="scmpds_2.html#K2">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E2:18"><i><font color="Green">E19</font></i></a>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><a NAME="E3:18_1"/><i><font color="Green">E26</font></i>: 
1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmpds_2.html#K3">DataLoc</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E3:18"><i><font color="Green">E20</font></i></a>, <a class="txt" href="scpqsort.html#E1:18_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><a NAME="E4:18_1"/><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E4:18"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scpqsort.html#E1:18_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><a NAME="E5:18_1"/>
<font color="Maroon">c<sub>8</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>12</sub></font> <a href="scmpds_2.html#K2">.</a> <span class="p1">(<span class="default"><a href="scmp_gcd.html#K1">intpos</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="scpqsort.html#E4:18"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scpqsort.html#E1:18_1"><i><font color="Green">E24</font></i></a>, <a class="ref" href="scmpds_4.html#T23">SCMPDS_4:23</a></i>;<br/><b>hence </b><a NAME="E6:18_1"/>
 <a href="scmpds_8.html#K3">while&gt;0</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>12</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E1:18"><i><font color="Green">E18</font></i></a>, <a class="txt" href="scpqsort.html#E4:18"><i><font color="Green">E21</font></i></a>, <a class="txt" href="scpqsort.html#E5:18"><i><font color="Green">E22</font></i></a>, <a class="txt" href="scpqsort.html#E2:18_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="scpqsort.html#E3:18_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="scpqsort.html#E4:18_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="scpqsort.html#E16"><i><font color="Green">Lemma16</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:18"/>
 <a href="scmpds_8.html#K3">while&gt;0</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="scmpds_6.html#R2">is_halting_on</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>thus </b><a NAME="E8:18"/>
 <a href="scmpds_8.html#K3">while&gt;0</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="scmpds_6.html#R1">is_closed_on</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="scpqsort.html#E6:18"><i><font color="Green">E23</font></i></a>, <a class="ref" href="scpqsort.html#T3" target="_self">Th3</a></i>;<br/>


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