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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="ordinal1.html#V7">natural</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="setfam_1.html#V1">with_non-empty_elements</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="struct_0.html#V3">empty</a> non <a href="ami_1.html#V2">void</a> <a href="ami_1.html#V5">IC-Ins-separated</a> <a href="ami_1.html#V8">definite</a> <a href="amistd_1.html#V4">standard</a>  <a href="ami_1.html#L1">AMI-Struct</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="ami_1.html#M1">FinPartState</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>







<a NAME="E1:17"/><i><font color="Green">E14</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> where B is   <a href="nat_1.html#NM1">Nat</a> :  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="amistd_2.html#D16">AMISTD_2:def 16</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a>
<div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:17_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E3:17_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E4:17_1"/><i><font color="Green">E16</font></i>: 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="scmring4.html#E1:17"><i><font color="Green">E14</font></i></a></i>;<br/><span class="p1">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="amistd_1.html#K8">+</a> <font color="Maroon">c<sub>1</sub></font> = 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <span class="p3">(<span class="default"><a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_1.html#D14">AMISTD_1:def 14</a></i>
<br/>.= 
 <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a></i>
;<br/><b>hence </b><a NAME="E6:17_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> where B is   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>3</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> </span>}</span> 
 <b>by </b><i><a class="txt" href="scmring4.html#E3:17_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="scmring4.html#E4:17_1"><i><font color="Green">E16</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E3:17"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> where B is   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>3</sub></font> : <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="ami_1.html#NM2">Instruction-Location</a> of <font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E5:17"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E6:17"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>
<a NAME="E7:17"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="amistd_1.html#K8">+</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="amistd_1.html#K7">locnum</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="amistd_1.html#D13">AMISTD_1:def 13</a>, <a class="ref" href="amistd_1.html#D14">AMISTD_1:def 14</a></i>;<br/>
<b>hence </b><a NAME="E8:17"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="amistd_2.html#K10">Shift</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scmring4.html#E1:17"><i><font color="Green">E14</font></i></a>, <a class="txt" href="scmring4.html#E5:17"><i><font color="Green">E15</font></i></a>, <a class="txt" href="scmring4.html#E6:17"><i><font color="Green">E16</font></i></a></i>;<br/>


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