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<b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/>

<b>assume </b><a NAME="E1:11"/><i><font color="Green">E10</font></i>: 
 <a href="ami_4.html#K1" target="_self">Euclide-Algorithm</a>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>13</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<a NAME="E2:11"/><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>14</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>15</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<b>assume </b><a NAME="E3:11"/>
 <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="ami_3.html#K16">il.</a> 4
 ;<br/>

<a NAME="E4:11"/><b>then </b>
<font color="Maroon">c<sub>13</sub></font> <a href="ami_3.html#R2">halts_at</a>  <a href="ami_1.html#K6">IC</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>14</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="ami_4.html#E1:11"><i><font color="Green">E10</font></i></a>, <a class="txt" href="ami_4.html#E6"><i><font color="Green">Lemma4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:11"/>
<span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>14</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>15</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="ami_1.html#K10">Computation</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="ami_1.html#K11">.</a> <font color="Maroon">c<sub>14</sub></font>
 <b>by </b><i><a class="txt" href="ami_4.html#E2:11"><i><font color="Green">E11</font></i></a>, <a class="ref" href="ami_3.html#T46">AMI_3:46</a></i>;<br/>


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